Combined thermocapillary-buoyancy convection has been investigated numerically in an extended cavity with differently heated walls. When the Marangoni number Ma grows, the unicellular flow is replaced by a steady bicellular or multicellular flow and then either by a hydrothermal wave or an oscillatory multicellular flow, depending on the dynamic Bond number Bo(dyn). The appearance of a hydrothermal wave prevents the propagation of the stationary roll structure, which spreads from the hot side, over the whole cavity. The hydrothermal wave itself looks as a succession of the cells moving from the cold side towards the motionless rolls on the hot side. For an intermediate interval of Bo(dyn) the parallel flow is unstable with respect to the hydrothermal wave (HTW), but the multicellular periodic structure generated by the side-wall perturbation is stable, so that the HTW decays in space when propagating on the background of the multicellular structure. The nonlinear competition between finite-amplitude, boundary-induced steady patterns and hydrothermal waves is essential. A nonlinear simulation of flow regimes in a wide region of the values of dynamical Bond number and Marangoni number is presented. A number of phenomena that cannot be predicted in the framework of the linear stability theory, specifically those characteristic for the motion in the intermediate interval of Bo(dyn), as well as the secondary transition from steady to unsteady flows at large Bo(dyn), which takes place when the Marangoni number Ma grows, are described.