We present the first experiments on electrohydrodynamic convection with a s
uperposed Couette shear in freely suspended annular smectic C* films. Simil
ar experiments on smectic A films have been carried out previously. In thos
e experiments, surface-charge driven electroconvection in combination with
shear leads to a pattern of travelling convective vortices. Travelling vort
ex patterns are also observed in smectic C* films. In contrast to smectic A
films, however, the flow field in C* films is coupled to c-director orient
ation effects that allow a direct visualization of the periodic flow patter
n. The critical voltage for the onset of convection was determined by elect
ric current measurements and compared with corresponding results for smecti
c A films. Measurements at various shear rates show that the onset is suppr
essed by the shear.