The double diffusive layer formation process in a laterally heated liquid layer which is stably stratified through a constant vertical salinity gradient is considered. The salt field is fixed at the horizontal boundaries to allow for steady solutions. The structure of stationary solutions and their linear stability is determined using continuation methods. Boundaries between different flow regimes, as observed experimentally, are to some extent identified as paths of particular bifurcation points. Using time integrations it is shown that unstable steady-states are physically relevant because the time at which the particular instability sets in may be very long.