Mixtures of symmetric distributions, in particular normal mixtures as a tool in statistical modeling, have been widely studied. In recent years, mixtures of asymmetric distributions have emerged as a top contender for analyzing statistical data. Tukey’s<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>family of generalized distributions depend on the parameters, namely,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>, which controls the skewness. This paper presents the probability density function (pdf) associated with a mixture of Tukey’s<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>family of generalized distributions. The mixture of this class of skewed distributions is a generalization of Tukey’s<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>family of distributions. In this paper, we calculate a closed form expression for the density and distribution of the mixture of two Tukey’s<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>families of generalized distributions, which allows us to easily compute probabilities, moments, and related measures. This class of distributions contains the mixture of Log-symmetric distributions as a special case.