We present the results of an experimental study of convective instabilities in a horizontal liquid layer with free upper surface under the action of an inclined temperature gradient, i.e., when horizontal and vertical temperature gradients are applied at the same time. Silicone oil of 10 cSt (Prandtl number Pr = 102) was employed as the test fluid. We investigated the layers with different thicknesses to examine the influence of gravity on the formation of the convective patterns. It is found out that the system behavior appreciably depends on the dynamic Bond number, which shows a relation of buoyancy and thermocapillary forces. In the case of small dynamic Bond numbers, when the influence of buoyancy is minimal, four different flow patterns, according to the combination of the vertical and horizontal Marangoni numbers, have been found: steady parallel flow, Bénard–Marangoni cells, drifting Bénard–Marangoni cells, and longitudinal rolls. At larger dynamic Bond number, when the influence of buoyancy becomes considerable, new convective structures, named by us the “surface longitudinal rolls” and the “surface drifting cells,” appear in addition to the patterns listed above. These instabilities exist only in the surface part of the thermocapillary flow, whereas the return flow remains stable. Under large enough dynamic Bond number these patterns become the dominating ones, forcing out the classical Bénard–Marangoni instability. We give a phenomenological description of the obtained convective patterns and present the stability diagram in the plane of the vertical and the horizontal Marangoni numbers.