An asymptotic analysis of the problem of unsteady-state heat and mass transfer of a droplet at commensurable phase resistances in the case of high Peclet numbers is carried out. The problem is considered in nonlinear statement when in the boundary condition of phase equilibrium on the droplet surface the concentration of a dispersed phase is arbitrarily dependent on continuous phase concentration. The dynamics of heat and mass transfer is shown to be qualitatively very different over three characteristic time intervals, the boundaries of which depend on Peclet number. The first time interval, 0 ⩽ t < O(ln Pe) ( t is the dimensionless time), is characterized by the formation of unsteady-state diffusional boundary layers on both sides of the droplet surface (which are as yet qualitatively identical), with the internal boundary layer generating a diffusional wake near the flow axis. Over the second time interval, O( ln Pe) ⩽ t < O(Pe), the developed internal diffusional wake starts to interact with the boundary layer and ‘smears’ it severely (here, the boundary layers outside and inside the droplet are already substantially different), as a result of which the thickness of the internal boundary layer increases considerably in a gradual way. Over the last time interval, 0( Pe) ⩽ t, a further rearrangement of the concentration field is observed so that the boundary layers are practically no longer present; the concentration outside the droplet becomes constant and equal to the nonperturbed concentration at infinity, while inside the droplet a substantially unsteady-state process occurs when concentration on each fixed streamline has already fully become equalized (at the expense of repeated liquid circulation along the closed streamlines), while mass is transferred by molecular diffusion in the direction normal to the streamlines.