In the limit of low Reynolds and Peclet numbers the motion of a drop in a solution of surfactant consumed on its surface in a chemical reaction is considered when, far off the drop in the outer fluid, there is a surfactant concentration and/or temperature gradient. It is shown that the chemical reaction can induce changes in the direction of the drop motion under the external concentration and/or temperature gradient. It can also induce multiple steady states of motion. For instance, for a given set of material and flow parameters and given external gradients and buoyancy, up to three regimes of drop motion may be available. Also a single value of the external gradient may stop the drop motion even for multiple (up to three) levels of buoyancy.