
440 S.E.2d 877 (1994)
JACKSON MILLS, INC., Respondent,
v.
BT CAPITAL CORPORATION, Appellant.
No. 23998.
Supreme Court of South Carolina.
Heard December 9, 1993.
Decided January 24, 1994.
*878 James M. Brailsford, III and Jacquelyn L. Bartley both of Robinson, McFadden & Moore, P.C., Columbia, for appellant.
Michael E. Spears, Spartanburg, for respondent.
CHANDLER, Acting Chief Justice:
BT Capital Corporation (BTC) appeals Circuit Court's order denying its motion to stay the present litigation pending arbitration.
We reverse.

FACTS
In 1983, Jackson Mills (JM) was formed with capital contributions from BTC, including BTC's purchase of 10,000 shares, representing 33.33% of JM's common stock. The Shareholder's Agreement (S/A), dated September 30, 1983, provided BTC the option to sell its outstanding shares to JM between October and December of 1991 at a price determined by a specified formula. The S/A was terminable "at any time by an instrument in writing signed by Shareholders holding 75% or more of the issued and outstanding common stock...." Finally, the S/A contains an Arbitration Clause, as follows:
Any controversy arising under, out of, in connection with, or relating to, this Agreement, and any amendment hereof, or the breach hereof, shall be determined and settled by arbitration in New York City.
In 1984 BTC sold 3,000 of its 10,000 shares back to JM, which reduced its proportionate common stock ownership to 23.33%.
On February 20, 1985, at the annual shareholder's meeting, 76.66% of the shareholders voted, orally, to terminate the S/A. BTC's representative abstained from the vote. The oral termination was not reduced to "an instrument in writing signed by the shareholders" as required by the S/A.
In August, 1987, BTC sold another 4,000 of its shares back to JM, leaving it with 3,000 shares.
In summer, 1991, JM was notified by its accountants that the 1985 termination of the S/A needed to be in writing and signed. Thereafter, BTC refused to sign a Termination Agreement, claiming the 1983 S/A was still in effect. On October 9, 1991, BTC advised JM that it was exercising its option to sell its remaining 3,000 shares pursuant to the S/A.
*879 JM instituted this declaratory judgment action seeking a ruling that the 1983 S/A had been terminated and was therefore null and void. BTC responded, moving to stay the action pending arbitration, as provided for in the S/A. Circuit Court denied BT's motion to stay the action, holding the S/A was properly terminated on February 20, 1985, such that there was in existence no binding arbitration clause.

ISSUE
Did Circuit Court err in refusing to stay this action pending arbitration?

DISCUSSION
BTC contends that whether or not the Shareholder's Agreement was terminated is a matter to be resolved by arbitration. We agree.
Arbitration clauses are separable from the contracts in which they are imbedded. Prima Paint Corp. v. Flood & Conklin, 388 U.S. 395, 87 S.Ct. 1801, 18 L.Ed.2d 1270 (1967). We recently adopted the Prima Paint reasoning, stating that "a party cannot avoid arbitration through rescission of the entire contract when there is no independent challenge to the arbitration clause." South Carolina Public Service Authority v. Great Western Coal, Inc., 437 S.E.2d 22 (Sup.Ct., 1993) (Emphasis supplied).
Our holding in Great Western accords with the "general rule that the duty to arbitrate under an arbitration clause in a contract survives termination of the contract." State ex rel. Ranger Fuel Corp. v. Lilly, 165 W.Va. 98, 267 S.E.2d 435, 437 (1980) citing Mendez v. Trustees of Boston Univ., 362 Mass. 353, 285 N.E.2d 446 (1972); Application of Frank Chevrolet Corp., 32 Misc.2d 1057, 224 N.Y.S.2d 928 (1961); Better Building Materials Company v. Kirschner, 142 Conn. 1, 110 A.2d 464 (1954). Under a broad arbitration clause, termination of the parties' substantive obligations under the contract involves conduct and matters subsequent to contracting which are to be determined by an arbitrator. Feffer v. Goodkind, et al., 152 Misc.2d 812, 578 N.Y.S.2d 802 (1991); Brown v. V & R Advertising, 112 A.D.2d 856, 493 N.Y.S.2d 137 (1985); Matter of Estate of Cassone, 63 N.Y.2d 756, 480 N.Y.S.2d 317, 469 N.E.2d 835 (1984).
Here, JM does not allege termination of the arbitration clause itself, but of the entire S/A. BTC's primary contention is that JM's purported termination violates the S/A provision that any termination be in writing and signed by 75% of the stockholders. It is, therefore, a controversy "arising under, in connection with and relating to" the termination provision of the S/A, subject to arbitration.
Contrary to JM's contention, our holding today does not render arbitration agreements irrevocable under all circumstances. Clearly, an arbitration agreement itself is subject to termination, a fact contemplated by S.C.Code Ann. § 15-48-10(a) which provides:
A written agreement to submit any existing controversy to arbitration or a provision in a written contract to submit to arbitration any controversy thereafter arising between the parties is valid, enforceable and irrevocable, save upon such grounds as exist at law or in equity for the revocation of any contract. (Emphasis supplied).
However, it is only when a party has valid grounds upon which to challenge the arbitration clause itself that arbitration may be avoided. See U.S. Insulation, Inc. v. Hilro Const. Co., 146 Ariz. 250, 705 P.2d 490 (AZ App.1985). For example, a party may claim the controversy arose out of events occurring subsequent to expiration of the arbitration agreement itself, or a party may allege that the arbitration agreement was never entered into. Under such circumstances, a challenge to the existence of the arbitration agreement itself becomes a matter to be "forthwith and summarily tried" by the Court. Prima Paint, supra; S.C.Code Ann. § 15-48-20(a) and (b) (Supp.1992).
Here, there is no challenge to the arbitration agreement itself; the controversy clearly arises under the provisions of the parties' S/A. Circuit Court erred in refusing to stay the present litigation pending arbitration.
REVERSED.
*880 FINNEY, TOAL and MOORE, JJ., and L. HENRY McKELLAR, Acting Associate Justice, concur.
