In the mixture transition distribution (MTD) model the time series \(X_1\),…, \(X_n\),…of random variables taking values in a finite set is considered as an \(h\)-order Markov chain with transition probabilities \[ \Pr\{X_t=i_0 |X_{t-1}=i_1,\dots, X_{t-l}=i_l\} =\sum_{g=1}^l \phi_g q_{i_g i_0}, \] where \(Q=[q_{ij}]\) is a transition matrix and \(\phi=(\phi_1,\dots,\phi_l)\) is a vector of lag “mixing probabilities”. \(Q\) and \(\phi\) are unknown and should be estimated by the observations \(X_1\),…,\(X_n\). The author proposes a new iterative procedure of local log-likelihood maximization and technology of initial values selection for this algorithm. Two generalizations of MTD are discussed: MTDg at which \(Q\)-matrices are different for different lags and a spatial model based on the concept of Markov random fields. The algorithms are applied to data of, e.g., DNA sequences of mouse \(\alpha\)A-crystallin gene analysis.