Convexity and smoothness are often too strong assumptions for the needs of Applications for instance in mathematical economics. Recently much attention Has been given to special dir=rtl align=right Wich could serve as substitutes to these assumptions. Here we focus on approximately Convex functions. Most of the existing results characterizing these dir=rtl align=right Established for locally lipschitzian functions. It is shown that a locally lipschitz function Is approximately convex if and only if its subdifferential is a submonotone operator. We stress the case of lower semicontinuous functions. Convex functions have far-reaching Consequences in the study of optimization problems and have been used in both theoretical And practical purposes. We will relate the notion of approximate convexity to the notion Of approximate monotonicity through the use of subdifferentials and generalized directional Derivaties for the relationships between paraconvexity and paramonotonicity.