We present an approach for the cross-lingual induction of speech recognition grammars that separates the task of translation from the task of grammar generation. The source speech recognition grammar is used to generate phrases, which are translated by a common translation service. The target recognition grammar is induced by using the production rules of the source language, manually translated sentences and a statistical word alignment tool. We induce grammars for the target languages Spanish and Japanese. The coverage of the resulting grammars is evaluated on two corpora and compared quantitatively and qualitatively to a grammar induced with unsupervised monolingual grammar induction.