This paper introduces Stochastic Definite Clause Grammars, a stochastic variant of the well-known Definite Clause Grammars. The grammar formalism supports parameter learning from an-notated or unannotated corpora and provides a mechanism for parse selection by means of sta-tistical inference. Unlike probabilistic context-free grammars, it is a context-sensitive gram-mar formalism and it has the ability to model cross-serial dependencies in natural language. SDCG also provides some syntax extensions which makes it possible to write more compact grammars and makes it straight-forward to add lexicalization schemes to a grammar.