The paper present a proposed approach in the context-free language theory. The main new notion is a graph defining a pushdown automaton (PDA). Each vertex of such graph is a pair (state, stack symbol). Each edge corresponds to a “command” and is labelled by input portion being read by the command and by a “charge” describing the stack word transformation. Some paths of the graph represent PDA's computations. The finite automata are a case of the pushdown graphs. The paper contains some of the author's results based on the approach – the notion of a D-language extending the notion of Dyck's language and the theorem on a representation of a context-free language as a morphical image of the intersection of a D-language with a local set.