  The purpose of this paper is to establish a very general Cameron-Storvick
theorem involving the generalized analytic Feynman integral of functionals on
the product function space $C_{a,b}^2[0,T]$. The function space $C_{a,b}[0,T]$
can be induced by the generalized Brownian motion process associated with
continuous functions $a$ and $b$. To do this we first introduce the class
$\mathcal F_{A_1,A_2}^{\,\,a,b}$ of functionals on $C_{a,b}^2[0,T]$ which is a
generalization of the Kallianpur and Bromley Fresnel class $\mathcal
F_{A_1,A_2}$. We then proceed to establish a Cameron-Storvick type theorem on
the product function space $C_{a,b}^2[0,T]$.
  Finally we use our Cameron--Storvick type theorem to obtain several
meaningful results and examples.
