We utilize stroboscopic optical microscopy to monitor the shear induced deformation of polymeric droplets in an immiscible polymeric matrix and find that under conditions of high droplet elasticity, the droplets can align in the vorticity direction. We consider the case where the viscosity ratio of the two phases is near unity but the elasticity ratio of the droplet to the matrix is greater than 100. This is achieved by using a matrix phase of polydimethylsiloxane and a droplet phase of a polyisobutylene based "Boger" fluid. In the limit of weak shear and small droplets, the droplet alignment is along the shear direction, whereas for strong shear and large droplets, the alignment is along the vorticity direction. There is a range of conditions for which alignment can be along either axis. For droplets aligned along the vorticity axis, the distribution of aspect ratios is broad. The kinetic transformation from droplet flow alignment to vorticity alignment upon increase of shear flow has been observed, as well as the relaxation back to a spherical shape upon cessation of shear. We deduce from the kinetic experiments that the thickness in the gradient direction is less than that in the flow and vorticity directions. (C) 2000 The Society of Rheology. [S0148-6055(00)00202-9].