By introducing some appropriate definitions for Ulam type stabilities, in this paper, we discuss the Ulam and Hyers and the generalized Ulam and Hyers stabilities for two different classes of nonlinear singular fractional integro-differential problems of Lane and Emden type. The existence and uniqueness results for our two classes have already been published respectively in Math. Method. Appl. Sci., 2020, and Moroc. J. Pure Appl. Anal., 2020.