Fuzzy description logics (FDLs) are knowledge representation formalisms capable of dealing with imprecise<lb>knowledge by allowing intermediate membership degrees in the interpretation of concepts and roles. One<lb>option for dealing with these intermediate degrees is to use the so-called Gödel semantics, under which<lb>conjunction is interpreted by the minimum of the degrees of the conjuncts. Despite its apparent simplicity,<lb>developing reasoning techniques for expressive FDLs under this semantics is a hard task.<lb>In this paper, we introduce two new algorithms for reasoning in very expressive FDLs under Gödel<lb>semantics. They combine the ideas of a previous automata-based algorithm for Gödel FDLs with the known<lb>crispification and tableau approaches for FDL reasoning. The results are the two first practical algorithms<lb>capable of reasoning in infinitely valued FDLs supporting general concept inclusions.