Summary: The purpose of the present paper is to introduce two novel subclasses \({\mathcal T}_\mu(n,\lambda,\alpha)\) and \({\mathcal H}_\mu(n, \lambda,\alpha;\kappa)\) of analytic and univalent functions with negative coefficients, involving Ruscheweyh derivative operator. The various results investigated in this paper include coefficient estimates, distortion inequalities, radii of close-to-convexity, starlikenes, and convexity for the functions belonging to the class \({\mathcal T}_\mu(n,\lambda,\alpha)\). These results are then appropriately applied to derive similar geometrical properties for the other class \({\mathcal H}_\mu(n, \lambda,\alpha;\kappa)\) of analytic and univalent functions. Relevant connections of these results with those in several earlier investigations are briefly indicated.