An analysis is made for the transient response behavior of thermal or concentration boundary layers of a fluid sphere moving at constant velocity with internal circulation in another fluid of large extent under the condition of large Reynolds and Peclet numbers. The disturbance is initiated by a step change in temperature or solute concentration of either the continuous or disperse region fluids. The governing energy or mass conservation equations are solved using similarity transformations. The result shows that the growth of the boundary layers is independent of the fluid properties but is governed by a single parameter; namely, the product of the translating speed and time divided by the droplet radius. For all practical purposes, the transients will die out when the value of that parameter attains unity.