The boundary layer equations have been derived in terms of a general orthogonal curvilinear co-ordinate system in order to predict local rates of mass or heat transfer from any axisymmetric body rotating in axial flow. Substitution of suitable power series forms for velocity components, concentration (or temperature) distribution and scale factors reduced these equations to three infinite sets of ordinary differential equations. The two coupled infinite sets of hydro-dynamic equations were dependent on shape and on spin parameter (a measure of the rotational velocity of the body compared with the main stream velocity). The mass (or heat) transfer sets were dependent on shape and Schmidt (or Prandtl) number. The first pair of hydrodynamic equations were non-linear and their solution was obtained for spin parameters below ten using a finite difference technique. For higher spin parameters it was found necessary to use the technique of quasilinearisation. The remaining sets of hydrodynamic equations and the transfer equations were linear and were solved using the principle of super-position. A computer programme was produced to generate and solve the general equations of these sets. The analysis was used to study the effect of rotation on local rates of mass transfer from spheres, disks and spheroids with width to height ratios of 10/16 and 7/16. Solutions were obtained for the first five sets of the ordinary differential equations at spin parameters from zero to twenty and at Schmidt numbers from 0.7 to 10.0, the effect of rotation at infinite Schmidt number was also studied. The results obtained showed that local rates of mass transfer increased substantially with increasing spin parameter. The analysis was extended to predict local transfer rates from any axisymmetric body rotating in a quiescent fluid. In this case local and overall mass transfer numbers have been obtained for the sphere, 13/16 and 10/16 spheroids at Schmidt numbers of 0.7 to 100.0.