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This paper demonstrates that the theory of Stieltjes- Volterra integral equations may be subsumed in Mac Nerney's general integral equation theory by making suitable choices of linear spaces and sets of operators. Introduction. Our object is to obtain solutions of nonlinear integral equations of the form h(t) =f(t)-r-(L)f'cdF(t, )h using the theory of the product integral developed by Mac Nerney and Neuberger in (3), (4), and (5). This approach specialized to the linear case may be contrasted with that of Hinton (l). Suppose that 5 is a compact number-interval with the usual order denoted by 0 and {X, \\ -\\ \ is a complete normed linear space with zero element 0. Let M denote the class of all functions from X to X to which {0, 0} belongs and 1 the identity function in M. Let ffi be the set of all functions F from SXS into M such that

A product integral solution of a Stieltjes-Volterra integral equation.