We present a hierarchical statistical machine translation system which supports discontinuous constituents. It is based on synchronous linear context-free rewriting systems (SLCFRS), an extension to synchronous context-free grammars in which synchronized non-terminals span k≥ 1 continuous blocks on either side of the bitext. This extension beyond contextfreeness is motivated by certain complex alignment configurations that are beyond the alignment capacity of current translation models and their relatively frequent occurrence in hand-aligned data. Our experiments for translating from German to English demonstrate the feasibility of training and decoding with more expressive translation models such as SLCFRS and show a modest improvement over a context-free baseline.