GaN materials alloyed with group V anions form the so-called highly mismatched alloys (HMAs). Recently, the authors succeeded in growing N-rich GaNAs and GaNBi alloys over a large composition range by plasma-assisted molecular beam epitaxy (PA-MBE). Here, they present first results on PA-MBE growth and properties of N-rich GaNSb and InNAs alloys and compare these with GaNAs and GaNBi alloys. The enhanced incorporation of As and Sb was achieved by growing the layers at extremely low growth temperatures. Although layers become amorphous for high As, Sb, and Bi content, optical absorption measurements show a progressive shift of the optical absorption edge to lower energy. The large band gap range and controllable conduction and valence band positions of these HMAs make them promising materials for efficient solar energy conversion devices