We study some mathematical properties of a new generator of continuous distributions with two additional shape parameters called the Zografos-Balakrishnan odd log-logistic family. We present some special models and investigate the asymptotes and shapes. The density function of the new family can be expressed as a mixture of exponentiated densities based on the same baseline distribution. We derive a power series for its quantile function. Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Shannon and Rényi entropies and order statistics, which hold for any baseline model, are determined. We estimate the model parameters by maximum likelihood. Two real data sets are used to illustrate the potentiality of the proposed family