The role of language models in SMT is to promote fluent translation output, but traditional n-gram language models are unable to capture fluency phenomena between distant words, such as some morphological agreement phenomena, subcategorisation, and syntactic collocations with string-level gaps. Syntactic language models have the potential to fill this modelling gap. We propose a language model for dependency structures that is relational rather than configurational and thus particularly suited for languages with a (relatively) free word order. It is trainable with Neural Networks, and not only improves over standard n-gram language models, but also outperforms related syntactic language models. We empirically demonstrate its effectiveness in terms of perplexity and as a feature function in string-to-tree SMT from English to German and Russian. We also show that using a syntactic evaluation metric to tune the log-linear parameters of an SMT system further increases translation quality when coupled with a syntactic language model.