Osmophoresis denotes the motion of cells or small capsules in concentration gradients. When a fluid particle encapsulated in a semi-permeable membrane is placed in a solution having non-uniform concentration the particle responds to the local osmotic differences. It may shrink or swell and it may move from its initial position depending on the external concentration field. The quasi-steady analysis of osmophoretic motion of a rigid spherical capsule in a constant gradient presented by Anderson is extended to consider the more realistic case in which the encapsulating membrane is deformable. The model considers the combined effects of local osmotic pressure difference and local normal stress component and integrates a simultaneous solution of the dow field and the surface deformation. We consider uniform and non-uniform concentration. fields having zero and constant gradients, respectively. Various membrane properties and shapes and their influences are examined. In uniform concentrations the capsule goes through a single stage of adjustment of the shape to the developing concentration and stress differences. In fields with concentration gradients the solution indicates a three stage dynamics. A stage dominated by swelling, a stage of advance in the concentration field and a stage dominated by deformation during which the motion ceases. Osmophoresis of deformable particles appears to be a transient phenomenon.