
472 So.2d 1152 (1985)
Jerrold YOUNG, Petitioner,
v.
Fern ALTENHAUS, Respondent.
John E. MATHEWS, et ux., Petitioners,
v.
Glenn L. POHLMAN, etc., et al., Respondents.
Nos. 64504, 64589.
Supreme Court of Florida.
May 2, 1985.
*1153 James C. Blecke of Blackwell, Walker, Gray, Powers, Flick and Hoehl, Miami, for Jerrold Young, petitioner.
Peter S. Schwedock of Pelzner, Schwedock, Finkelstein and Klausner, Miami, for Fern Altenhaus, respondent.
R.J. Beckham of Beckham, McAliley and Schulz, Jacksonville, for John E. Mathews, et ux., petitioners.
John F. Corrigan and Lori E. Terens of Ulmer, Murchison, Ashby, Taylor and Corrigan, Jacksonville, for Joseph J. Lowenthal, M.D., Lowenthal & Puestow, P.A., and Florida Physicians' Insurance Reciprocal, respondents.
Pattillo and McKeever, P.A., Ocala, for Glenn L. Pohlman, M.D., Vinod D. Deshmukh, M.D., Jacksonville Neurological Clinic, P.A., and Florida Physicians' Insurance Reciprocal, respondents.
OVERTON, Justice.
These two cases are before the Court upon petitions for review of decisions of two district courts of appeal reported as Young v. Altenhaus, 448 So.2d 1039 (Fla. 3d DCA 1983), and Pohlman v. Mathews, 440 So.2d 681 (Fla. 1st DCA 1983). Each district court upheld the validity of section 768.56, Florida Statutes (1981), which authorizes the trial court to award a reasonable attorney's fee to the prevailing party in a malpractice action.[*]
We have upheld the constitutionality of section 768.56 in Florida Patient's Compensation Fund v. Rowe, 472 So.2d 1145 (Fla. 1985), released simultaneously with this opinion. These two cases present the question of whether section 768.56 applies to causes of action that accrued prior to that statute's effective date. For the reasons expressed below, we find that the assessment of attorney fees under section 768.56 is not applicable to these causes of action.
The following are the relevant facts in each of these cases.

Young v. Altenhaus
Altenhaus, the plaintiff in the trial court, prevailed in a malpractice action against Young, who is a physician, and another physician. The malpractice incident occurred in 1979, which was prior to the effective date of section 768.56. The trial court assessed attorney fees against the two physicians in the amount of $10,000 under the authority of section 768.56. Young challenged the constitutionality of the attorney fee statute in both the trial court and the district court on due process and equal protection grounds. The district court upheld the validity of the statute and the trial court's assessment of attorney fees.

Mathews v. Pohlman
Mathews was the plaintiff in the trial court, but lost in his malpractice action against Pohlman and other physicians. Mathews' cause of action accrued against the respondent physicians in 1978 and 1979 for alleged malpractice acts. The respondent physicians sought to recover $384,684 in attorney fees from Mathews pursuant to section 768.56 in the trial court. The trial court refused to apply the statute and found it violated the constitutional guarantees of equal protection, due process, and access to the courts. The district court reversed, upheld the constitutionality of the statute, and remanded the cause for proceedings to assess attorney fees. It *1154 certified to this Court the question of the constitutional validity of the attorney fee statute.

Applicability of Section 768.56 to Causes of Action Accruing Prior to its Effective Date.
As noted, we have upheld the constitutionality of section 768.56 in Rowe. In that case, it was not clear whether the cause of action accrued after the effective date of the section. In the instant cases, however, the record reveals that the causes of action accrued prior to the effective date. We must answer the question of whether section 768.56 may properly apply where the cause of action accrued prior to July 1, 1980, the date the section became effective. That section provides that it "shall not apply to any action filed before July 1, 1980." In each case, the plaintiff's action was filed after July 1, 1980, but the cause of action actually accrued before that date.
In Florida, it is clear that in the absence of an explicit legislative expression to the contrary, a substantive law is to be construed as having prospective effect only. State v. Lavazzoli, 434 So.2d 321 (Fla. 1983); Seddon v. Harpster, 403 So.2d 409 (Fla. 1981); Trustees of Tufts College v. Triple R Ranch, Inc., 275 So.2d 521 (Fla. 1973). This rule mandates that statutes that interfere with vested rights will not be given retroactive effect. On the other hand, statutes which relate only to the procedure or remedy are generally held applicable to all pending cases. In McCord v. Smith, 43 So.2d 704 (Fla. 1949), we stated:
A retrospective provision of a legislative act is not necessarily invalid. It is so only in those cases wherein ... a new obligation or duty is created or imposed ... in connection with transactions or considerations previously had or expiated.
Id. at 709 (emphasis added). As we explained in Rowe, the American Rule adopted in Florida requires each side to pay its own attorney's fee unless directed otherwise by a statute or an agreement between the parties. Given this rule of law, we find that a statutory requirement for the non-prevailing party to pay attorney fees constitutes "a new obligation or duty," and is therefore substantive in nature. See Whitten v. Progressive Casualty Insurance Co., 410 So.2d 501 (Fla. 1982). In the instant cases, Altenhaus' and Mathews' rights to enforce their causes of actions for malpractice against the defendants below vested prior to the effective date of the section 768.56. When these causes of action accrued, neither party was statutorily responsible for the opposing party's attorney's fee nor entitled to such an award. We agree with the First District Court of Appeal's recent decision in Parrish v. Mullis, 458 So.2d 401 (Fla. 1st DCA 1984), in which that court stated:
When appellant's cause of action accrued, she was not burdened with the potential responsibility to pay the successful party's attorney's fees and costs, and appellee was not entitled to that right. The right and responsibility were later created by the legislature... . [W]e hold that section 768.56 may not be retroactively applied to a cause of action which accrued prior to its effective date.
Id. at 402. The decision of the Second District Court of Appeal in Tindall v. Miller, 463 So.2d 1262 (Fla. 2d DCA 1985), is consistent with this holding. The Fourth District Court of Appeal has taken a contrary position in Frankowitz v. Propst, 464 So.2d 1225 (Fla. 4th DCA 1985), and Bethesda Radiology Associates, P.A. v. Yaffee, 437 So.2d 189 (Fla. 4th DCA 1983). We agree with the First and Second District Courts of Appeal that section 768.56 cannot be constitutionally applied to causes of action which accrued prior to July 1, 1980.
Accordingly, we quash the portions of the opinions of the district courts of appeal in the instant cases holding that attorney fees may be awarded to the prevailing parties pursuant to section 768.56. We remand Mathews with direction to enter a judgment in accordance with this opinion. No remand is necessary in Young because that cause has been settled by stipulation pending its review in this Court. We approve *1155 Parrish and Tindall, and we disapprove the portions of Frankowitz and Bethesda Radiology in which the court affirmed the retroactive application of the subject statute.
It is so ordered.
BOYD, C.J., and ADKINS, ALDERMAN, McDONALD and SHAW, JJ., concur.
EHRLICH, J., did not participate in the consideration of these cases.
NOTES
[*]  We have jurisdiction pursuant to article V, section 3(b)(3), Florida Constitution. In addition, in Mathews, the district court certified to this Court the following question as being of great public importance: "Does section 768.56, Florida Statutes, violate constitutional guarantees of equal protection, due process, or access to the courts?" 440 So.2d at 683.
