We reveal the existence of stable dissipative soliton complexes with curvilinear motion of their center of mass. This type of motion results from the field distribution asymmetry and is well pronounced for asymmetric complexes of laser solitons with strong coupling. We present results of numerical simulations of such complexes in a model of wide-aperture lasers or laser amplifiers with saturable gain and absorption. The complex consists of a pair of strongly coupled vortex solitons weakly coupled with a number of other vortex solitons. Similar complexes are expected to exist in different spatially distributed nonlinear dissipative systems, including schemes with discrete dissipative solitons.