We propose a new method of adding two parameters to a continuous distribution that extends the idea first introduced by Lehmann (1953) and studied by Nadarajah and Kotz (2006). This method leads to a new class of exponentiated generalized distributions that can be interpreted as a double construction of Lehmann alternatives. Some special models are discussed. We derive some mathematical properties of this class including the ordinary moments, generating function, mean deviations and order statistics. Maximum likelihood estimation is investigated and four applications to real data are presented.