<p>The Roche potential plays a pivotal role in studying the problems of rotating stars and stars in the close binary systems. The standard or classical expression of Roche potential considers the effects of gravitational and centrifugal forces and excludes the effect due to various other forces. However, certain authors have modified the standard expression of Roche potential by including the effects of radiation pressure, nonsynchronous rotation, eccentricity of the orbits, non-uniform rotation and misaligned axis of rotation and revolution. In these studies, the modification have been incorporated in the expression of standard Roche potential by considering either one or at most two effects. In this paper we have obtained a more generalized expression of Roche potential that considers more than two effects, including the radiation pressure, nonsynchronous rotation and eccentricity of the orbits. This expression has been then used to determine the effect of radiation pressure, nonsynchronous rotation, and eccentricity on the position of the colinear Lagrangian points, and corresponding Roche potential in close binary system of stars, The result of the present study shows that when the effects of radiation pressure, nonsynchronous rotation and eccentricity are considered then there is an appreciable change in the position of colinear Lagrangian points and corresponding Roche potential of the stars in close binary systems.</p>