The solar galactic neighborhood contains a number of young co-moving associations of stars (known as young moving groups) with ages of similar to 10-150 Myr, which are prime targets for a range of scientific studies, including direct imaging planet searches. The latetype stellar populations 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 e ff ort to identify new close binaries in nearby young moving groups, through highresolution 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. An interesting example of such a case is 2MASS J00302572-6236015 AB, which is a high-probability member of the Tucana-Horologium moving group, and has an estimated orbital period of less than 10 yr. Among the previously known objects is a serendipitous detection of the deuterium burning boundary circumbinary companion 2MASS J01033563-5515561 (AB)b in the z' band, thereby extending the spectral coverage for this object down to near-visible wavelengths.