In a previous work, we developed a quasi-efficient maximum likelihood approach for blindly separating stationary, temporally correlated sources modeled by Markov processes. In this paper, we propose to extend this idea to separate mixtures of non-stationary sources. To handle non-stationarity, two methods based respectively on blocking and kernel smoothing are used to find parametric estimates of the score functions of the sources, required for implementing the maximum likelihood approach. Then, the proposed methods exploit simultaneously non-Gaussianity, nonstationarity and time correlation in a quasi-efficient manner. Experimental results using artificial and real data show clearly the better performance of the proposed methods with respect to classical source separation methods.