Let C [ 0 , T ] C[0,T] denote Wiener space, i.e., the space of all continuous functions η ( t ) \eta (t) on [ 0 , T ] [0,T] such that η ( 0 ) = 0 \eta (0) = 0 . For Q = [ 0 , S ] × [ 0 , T ] Q = [0,S] \times [0,T] let C ( Q ) C(Q) denote Yeh-Wiener space, i.e., the space of all R \mathbb {R} -valued continuous functions x ( s , t ) x(s,t) on Q Q such that x ( 0 , t ) = x ( s , 0 ) = 0 x(0,t) = x(s,0) = 0 for all ( s , t ) (s,t) in Q Q . For h ∈ L 2 ( Q ) h \in {L_2}(Q) let Z ( x ; s , t ) Z(x;s,t) be the Gaussian process defined by the stochastic integral \[ Z ( x ; s , t ) = ∫ 0 t ∫ 0 s h ( u , v ) d x ( u , v ) . Z(x;s,t) = \int _0^t {\int _0^s {h(u,v)dx(u,v).} } \] Then for appropriate functionals F F and ψ \psi we show that the operator-valued function space integral \[ ( I λ h ( F ) ψ ) ( η ( ⋅ ) ) = E x [ F ( λ − 1 / 2 Z ( x ; ⋅ , ⋅ ) + η ( ⋅ ) ) ψ ( λ − 1 / 2 Z ( x ; S , ⋅ ) + η ( ⋅ ) ) ] (I_\lambda ^h(F)\psi )(\eta ( \cdot )) = {E_x}[F({\lambda ^{ - 1/2}}Z(x; \cdot , \cdot ) + \eta ( \cdot ))\psi ({\lambda ^{ - 1/2}}Z(x;S, \cdot ) + \eta ( \cdot ))] \] is the unique solution of a Kac-Feynman Wiener integral equation. We also use this integral equation to evaluate various Yeh-Wiener integrals.