In this paper, we propose and study a new class of continuous distributions called the Marshall-Olkin exponentiated generalized G (MOEG-G) family which extends the Marshall-Olkin-G family introduced by Marshall and Olkin [A. W. Marshall, I. Olkin, Biometrika, 84 (1997), 641–652]. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, order statistics and probability weighted moments are derived. Some charac-terizations for the new family are presented. Maximum likelihood estimation for the model parameters under uncensored and censored data is addressed in Section 5 as well as a simulation study to assess the performance of the estimators. The importance and flexibility of the new family are illustrated by means of two applications to real data sets.