Simultaneous acoustic emission, AE, and DSC measurements under compression along [110]A direction were carried out on Ni49Fe18Ga27Co6 shape memory single crystals. The compression resulted in anomalous stress-strain loops with stress drops/jumps on it, reflecting a sudden formation/dissolution of a more stable (detwinned) martensite structural modification than the thermally induced (twinned) one. The final detwinned martensite, obtained below a certain temperature, was stable even after downloading: during heating it showed a burst-like recovery at about 35K higher transformation temperature than that of the thermally induced one, with an audible click. It was obtained that the number of acoustic events showed strong asymmetry: e.g. for stress induced transformations the number of hits for uploading was larger. Simultaneous measurements of stress-time curves and AE versus time revealed that in the nucleation/dissolution processes in both (up and down) directions, as an intermediate step, the twinned martensite was first formed and resulted in additional AE events. This was interpreted by the easy as well as difficult nucleation of the twinned and detwinned martensites, respectively. The stress drops on the uploading stress-strain curve were attributed to subsequent nucleation of the detwinned martensite from the twinned modification and were followed by a sharp decrease of the AE activity. This indicated that the formation of detwinned martensite is a sudden, fast process and can take place without significant elastic energy storage. This was also in agreement with the fact that during burst like thermal recovery the width of the transition was very small (Af≅ As). Similarly, during downloading the stress jumps were interpreted as sudden dissolutions of the detwinned phase by retwinning and at all stress jumps there were local maxima on the AE activity curve.