Unsteady state mass transfer between a one or two component bubble (or drop) and the continuous phase with a chemical reaction occuring either in the continuous or in the dispersed phase is examined. The main assumption for binary bubbles is that the rate determining step is diffusion in the continuous phase. Two limiting velocity fields. Hadamard flow ( Re⪡:1) and potential flow ( Re⪡:1) are used in the calculations. For the single component bubble the solution obtained previously by Ruckenstein for mass transfer without chemical reaction is generalized to include chemical reaction by using Danckwerts' transformation and the Duhamel theorem and relatively simple analytical expressions are deduced for transient and steady state average Sherwood numbers. For binary bubbles the concentration of the continuous phase depends on the dispersed phase concentration which is a function of time. Consequently the same procedure used for the single component case, together with a material balance on the bubble, generates an integral equations which is solved by an iterative technique for the concentration inside the bubble. To determine the accuracy of simplified models of the type suggested by Higbie an extended penetration model is proposed and used for the situation in which a chemical reaction occurs in the continuous phase. The results of the simplified model are compared with the exact solutions for one and two component systems, and the range of parameters for which it is accurate is determined. The accuracy of the quasi-steady state assumption, based on the steady state equations for the mass transfer coefficient and on an unsteady mass balance for the bubble, is also examined and it is shown that this assumption may introduce significant errors under certain conditions. Criteria giving the conditions under which the quasi-steady state assumption may be used are established.