Variations in the surface supersaturation sigma (s), caused by an abrupt (stepped) change in bulk supersaturation sigma and subsequent exponential decrease or increase in sigma, are studied with the use of the surface diffusion theory of Burton, Cabrera and Frank (BCF). The study is based on the analytical solution [M. Rak, Surf. Sci. 442 (1999) 149] of the BCF time-dependent equation. It is shown that the solution can be approximated by a simple expression convenient for the analysis. It is found that at the time t = 0, the instantaneous rate of a change in the surface supersaturation sigma (s) is determined only by the exchange of growth units between the crystal surface and the solution bulk, and is not affected by the surface diffusion. If an abrupt increase in bulk supersaturation a at t = 0 is followed by an exponential decrease in sigma, then at t(M) > 0 the function sigma (s) of t has a maximum. In the opposite case, i.e. if an abrupt decrease in sigma at t = 0 is followed by an exponential increase in sigma, then sigma (s) has a minimum at t(M) > 0. The time t(M) is estimated and an effect of variations in a on value of t(M) is analysed.