In this paper, we propose a discriminative counterpart of the directed Markov Models of order k - 1, or MM (k - 1) for sequence classification. MM(k - 1) models capture dependencies among neighboring elements of a sequence. The parameters of the classifiers are initialized to based on the maximum likelihood estimates for their generative counterparts. We derive gradient based update equations for the parameters of the sequence classifiers in order to maximize the conditional likelihood function. Results of our experiments with data sets drawn from biological sequence classification (specifically protein function and subcellular localization) and text classification applications show that the discriminatively trained sequence classifiers outperform their generative counterparts, confirming the benefits of discriminative training when the primary objective is classification. Our experiments also show that the discriminatively trained MM(k - 1) sequence classifiers are competitive with the computationally much more expensive Support Vector Machines trained using k-gram representations of sequences.