The solar galactic neighbourhood contains a number of young co-moving associations of stars (so-called 'young moving groups') with ages of ~10-150 Myr, which are prime targets for a range of scientific studies, including direct imaging planet searches. The late-type stellar population of such groups still remain in their pre-main sequence phase, and are thus well suited for purposes such as isochronal dating. Close binaries are particularly useful in this regard, since they allow for a model-independent dynamical mass determination. Here we present a dedicated effort to identify new close binaries in nearby young moving groups, through high-resolution imaging with the AstraLux Sur Lucky Imaging camera. We surveyed 181 targets, resulting in the detection of 61 companions or candidates, of which 38 are new discoveries.