Consider a symmetric bilinear form defined on $prod imesprod$ by $_{lambdamu}$ = $;+;lambdaL[f](a)L[g](a);+;muM[f](b)m[g](b)$ ,where $sigma$ is a quasi-definite moment functional, L and M are linear operators on $prod$, the space of all real polynomials and a,b,$lambda$ , and $mu$ are real constants. We find a necessary and sufficient condition for the above bilinear form to be quasi-definite and study various properties of corresponding orthogonal polynomials. This unifies many previous works which treated cases when both L and M are differential or difference operators. finally, infinite order operator equations having such orthogonal polynomials as eigenfunctions are given when $mu$=0.