In this paper, we study the effect of gravity, or buoyancy forces, on the structure of flames propagating in horizontal channels. It is shown that there are two mechanisms for the appearance of non-symmetric flames. The first, more obvious, is related to buoyancy, when a hotter gas of lower density tends to be located in the upper half of the channel. However, there is a second mechanism associated with the intrinsic flame instabilities, which also can cause the loss of flame symmetry. This mechanism can, at certain values of the parameters, act in the opposite direction, when hotter gases are enclosed in the lower part of the channel. In this case, two stable non-symmetric solutions may exist in the presence of gravitational forces and the establishment of one or another configuration depends on the initial conditions. The stability of these solutions is demonstrated by time-dependent computations.