Vortices are believed to greatly help the formation of km sized planetesimals by collecting dust particles in their centers. However,vortex dynamics is commonly studied in non-self-gravitating disks. The main goal here is to examine the effects of disk self-gravity on the vortex dynamics via numerical simulations. In the self-gravitating case,when quasi-steady gravitoturbulent state is reached, vortices appear as transient structures undergoing recurring phases of formation, growth to sizes comparable to a local Jeans scale, and eventual shearing and destruction due to gravitational instability. Each phase lasts over 2-3orbital periods. Vortices and density waves appear to be coupled implying that, in general, one should consider both vortex and density wave modes for a proper understanding of self-gravitating disk dynamics.Our results imply that given such an irregular and rapidly changing,transient character of vortex evolution in self-gravitating disks it maybe difficult for such vortices to effectively trap dust particles in their centers that is a necessary process towards planet formation.