
610 So.2d 20 (1992)
UNITED STATES MINERAL PRODUCTS COMPANY, et al., Appellants/Cross-Appellees,
v.
Thomas WATERS and Eloise Agnes Waters, his wife, Appellees/Cross-Appellants.
W.R. GRACE & CO. CONN., Appellants,
v.
Thomas WATERS and Eloise Agnes Waters, his wife, Appellees.
Nos. 90-1838, 90-2010 and 91-282.
District Court of Appeal of Florida, Third District.
November 24, 1992.
*21 Welcher & Clark and Roger G. Welcher, Miami, Nancy Little Hoffmann, Fort Lauderdale, for cross-appellees U.S. Mineral.
Kubicki, Draper, Gallagher & McGrane, Miami, for appellant W.R. Grace.
Colson, Hicks, Eidson, Colson & Matthews, Cooper & Wolfe, Marc Cooper and Maureen E. Lefebvre, Miami, for appellees/cross-appellants.
Before SCHWARTZ, C.J., and NESBITT and FERGUSON, JJ.
PER CURIAM.
These consolidated appeals arise from an order of final judgment rendered on a jury verdict in favor of Thomas Waters and Eloise Agnes Waters, in a personal injury action for damages caused by Thomas Waters' alleged occupational exposure to asbestos products. The Waters' cross-appeal the trial court's order dismissing from their amended complaint their causes of action sounding in strict liability and striking their claims for punitive damages. For the following reasons we affirm the final judgment but remand to the trial court for further proceedings consistent with this opinion.
Thomas Waters was employed as a tile setter from the late 1950's through 1988. He alleged that he had contracted pulmonary asbestosis in the lower part of his lungs as a result of exposure to asbestos-containing fireproofing products manufactured and sold by United States Mineral Products Company (USM) and W.R. Grace & Co. (Grace). He filed suit against the two companies, and the jury returned a verdict finding Grace 50% negligent, USM 40% negligent, and Mr. Waters 10% comparatively negligent. Adjusting for comparative negligence and setoffs, a final judgment was entered in favor of Mr. Waters for $446,594.10 and in favor of Mrs. Waters for $118,191.40.
On appeal, USM argues that it was entitled to a directed verdict because the evidence adduced at trial was insufficient to show that Mr. Waters was exposed to USM's asbestos product, and further, that there was insufficient evidence to demonstrate that Mr. Waters' exposure to its product contributed substantially to producing the injury complained of. Additionally, USM and Grace claim that the trial court erred in not granting their motions for mistrial when one of the plaintiffs' expert witnesses fainted shortly after taking the witness stand. We disagree on both points.
First, evidence was introduced at trial that Mr. Waters may have been exposed to USM's asbestos product at six specific construction sites where he had worked during the 1950's and 1960's. Exposure to the product could have occurred at any or all of those sites. Although USM points to discrepancies in Mr. Waters' trial and deposition testimony, whether the apparent conflicts had any affect on the credibility of his testimony, was a factor to be considered by the jury alone. Maas Bros., Inc. v. Bishop, 204 So.2d 16, 19 (Fla. 2d DCA 1967). Additionally, evidence presented at trial from two medical experts was sufficient to support a jury finding that Mr. Waters' exposure to USM's asbestos product proximately caused his injury. See generally Stahl v. Metropolitan Dade County, 438 So.2d 14 (Fla. 3d DCA 1983); see also Reaves v. Armstrong World Ind., Inc., 569 So.2d 1307 (Fla. 4th DCA 1990), review denied, 581 So.2d 166 (Fla. 1991). A directed verdict in USM's favor would thus have been improper.
Second, USM and Grace claim that they were entitled to a mistrial because they were never given the opportunity to cross examine a witness who fainted shortly after taking the witness stand. They also claim that the jury was prejudiced by witnessing the event. The judge specifically asked counsel if they felt prejudiced by not being able to cross-examine the witness. Attorneys for both USM and Grace agreed that no prejudice occurred since only background information had been elicited *22 from the witness prior to his fainting. Because the attorneys failed to object to not being able to cross-examine the witness at trial, this argument was not properly preserved, and the defendants may not argue it on appeal. See State v. Copelan, 466 So.2d 1133 (Fla. 1st DCA 1985); Diaz v. Rodriguez, 384 So.2d 906 (Fla. 3d DCA 1980).
Furthermore, whether a particular event requires a mistrial is a matter within the trial court's discretion. See, e.g., Compania Dominicana de Aviacion v. Knapp, 251 So.2d 18, 21 (Fla. 3d DCA), cert. denied, 256 So.2d 6 (Fla. 1971). In the instant case, the trial court questioned the members of the jury to determine if they had been prejudiced, and then instructed them that the incident should not affect their consideration of the case. The trial court did not abuse its discretion in concluding that USM and Grace had suffered no prejudice, and, thereafter, denying their motions for mistrial.
Finally, on cross-appeal, the Waters' argue that the trial court erred in dismissing their causes of action sounding in strict liability and in striking their claims for punitive damages against USM and Grace. The trial judge had apparently concluded that the strict liability theory was a duplication of the negligent failure-to-warn count and was, therefore, improper. When a set of facts will support both a theory of common law negligence and strict liability, a plaintiff is entitled to proceed on either theory or both. Ford Motor Co. v. Hill, 404 So.2d 1049 (Fla. 1981); Baione v. Owens-Illinois, Inc., 599 So.2d 1377 (Fla. 2d DCA 1992). Since injury from exposure to a product containing asbestos clearly falls within this category of cases, it was error to dismiss the counts in the complaint sounding in strict liability. West v. Caterpillar Tractor Co., Inc., 336 So.2d 80 (Fla. 1976); Baione, at 1378.
On the issue of punitive damages, the trial court granted USM's and Grace's motions to strike punitive damages on grounds that if a defendant has once had punitive damages assessed against it, it will no longer be subject to punitive damages. As recently stated by the Second District Court of Appeal:
We know of no authority which would support the striking of a claim for punitive damages, as a matter of law, for this sole-stated reason. To the contrary, punitive damages are appropriate in asbestos litigation and the trial court's reason, if relevant at all, would be an issue of mitigation to be considered by the trier of fact. See Johns-Manville Sales Corp. v. Janssens, 463 So.2d 242 (Fla. 1st DCA 1984), review denied, 467 So.2d 999 (Fla. 1985).
Baione, at 1378. As to USM, however, the Waters' have waived the issue of punitive damages since the order under appeal granted summary judgment only in Grace's favor on this issue. Since the Waters' did not present any evidence or request any jury instructions on punitive damages against USM, any claims they may have had on that issue are waived as to USM.
Accordingly, we affirm the final judgment awarding the Waters' damages against both USM and Grace. Additionally, we reinstate the strict liability count in the Waters' amended complaint, together with the claims for punitive damages against Grace only, and remand for further proceedings consistent with this opinion.
SCHWARTZ, C.J., and FERGUSON, JJ., concur.
NESBITT, Judge (concurring in part, dissenting in part):
I agree with the majority's opinion except that I would affirm the order striking the Waters' claims for punitive damages against W.R. Grace & Co. Since Grace has already had punitive damages assessed against it in other suits, I think the trial judge was eminently correct in striking the claim for punitive damages. The views of Judge Friendly expressed in Roginsky v. Richardson-Merrell, Inc., 378 F.2d 832, 838-42 (2d Cir.1967), pointing out the desirability of limiting multiple punitive damages awards, has proven its accuracy. Not only may such awards contribute to a company's bankruptcy, but they may result in *23 a denial of compensatory damages to victims whose injuries manifest at some later date. To continue to inflict punitive damages on a company for decisions which may have been made years earlier, is to perpetuate the sins of the boardroom, penalizing not only the shareholders but society as a whole, and deny the company its competitive place in the market.

CERTIFICATION OF QUESTION
NESBITT, FERGUSON, Judges, concurring.
The court sua sponte certifies to the Florida Supreme Court the question posed by the dissent as one of great public importance, pursuant to Florida Rule of Appellate Procedure 9.125(a).
SCHWARTZ, C.J., dissents.
