In the recent years, several new classes of contextual grammars have been introduced to give an appropriate model description to natural languages. With this aim, some new families of contextual languages have been introduced based on maximal and depth-first conditions and analyzed in the framework of so-called mildly context sensitive languages. However, the relationship among these families of languages have not yet been analyzed in detail. In this paper, we investigate the relationship between the families of languages whose grammars are based on maximal and depth-first conditions. We prove an interesting result that all these families of languages are incomparable to each other, but they are not disjoint. © 2009 Springer Berlin Heidelberg.