In the given article, enveloping C～*-algebras of AJW-algebras are considered. Conditions are given, when the enveloping C～*-algebra of an AJW-algebra is an AW～*-algebra, and corresponding theorems are proved. In particular, we proved that if A is a real AW～*-algebra, Asa is the JC-algebra of all self-adjoint elements of A, A + iA is an AW～*-algebra and A ∩ i A = {0} then the enveloping C～*-algebra C～*(A－（sa）) of the JC-algebra A—（sa） is an AW～*-algebra. Moreover, if A + iA does not have nonzero direct summands of type I—2, then C～*(A—（sa） coincides with the algebra A + iA, i.e. C～*(A—（sa）)= A + iA.
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