The stability of a fluid layer with adverse time‐dependent density gradients is examined by two computational techniques. The most direct solution, that of integrating the time‐dependent equations, is compared with the results obtained by invoking the often used quasistationary state approximation. It is seen that this latter approximation is not valid if the instability stems from a sudden change in the concentration or temperature at one surface of the fluid layer. The particular problem studied here is that of a liquid film resting on an impermeable wall with gas absorption into the liquid. In this case the system evolves from one stable state to another with the essential problem being to assess the stability of the system during its evolution between these stable states. It is shown that a single critical Rayleigh number does not exist as in the usual case with linear time‐independent density gradients, but that the critical Rayleigh number depends, to some extent, on intangible factors such as the initial perturbation magnitude and the mode of observation.