In this paper, we present a few results which are of interest for the potential application of contextual grammars to natural languages. We introduce two new classes of internal contextual grammars, called end-marked maximal depth-first and inner end-marked maximal depth-first contextual grammars. We analyze the new variants with respect to the basic properties of the mildly context sensitive languages. With this aim, we show that (i) the three basic non-context-free constructions in natural languages can be realized upon using these variants, (ii) the membership problem for these family of languages is decidable in polynomial time algorithm, (iii) the family of languages generated by end-marked maximal depth-first grammars contains non-semilinear languages. We also solve the following open problem addressed in [3] and [1]: whether the families of languages generated by maximal depth-first and maximal local contextual grammars are semilinear or not? © Springer-Verlag Berlin Heidelberg 2006.