In this paper we extend Floyd's notion of parsing by bounded context to define the Bounded Context Parsable Grammars, a class of recursive subsets of context free grammars for which we can construct linear time parsers. it is shown that the set of languages of the grammars thus defined properly contains the set of deterministic languages without the empty sentence. Keywords and Phrases: bounded context grammars, linear time parsers, deterministic context free languages.