For polynomials orthogonal on the radial rays in the complex plane, which were introduced in [12], we give first a short account, and then we develop two interesting classes of orthogonal polynomials: (1) the generalized Hermite polynomials; (2) the generalized Gegenbauer polynomials. For such polynomials we obtain the corresponding linear differential equations of the second order. Assuming a logarithmic potential, we give an electrostatic interpretation of the zeros of the generalized Gegenbauer polynomials.