Abstract: A class of close-to-convex functions is investigated, which is the generalization of the class of analytic functions whose derivatives have positive real parts. The following properties are discussed: distortion theorems, the radius of convexity, close-to-convexity of the partial sums and extremal functions.The subclass which contains functions with initial zero coefficients is also studied.

Key words: close-to-convex function, distortion theorem, radius of convexity, partial sum, extremal function