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In this paper we are studying the relations between generated and accepted hyperedge replacement languages. In context freeness of hyperedge replacement grammars we can transform each grammar into an equivalent one in Greibach Normal Form (HRGNF). In order to create a pushdown automata for hyperedge replacement languages (PDAH) we build an algorithm to transform the planar structure of a hypergraph into a linear list of labels and finally into a linear list of hypergraphs. With this kind of lists we can build a PDAH from existing HRGNF. For each grammar exists a PDAH which recognize the same language.