Low-stress creep measurements on a nematic liquid crystal polymer indicate that it is a viscoelastic solid, with a modulus of 100 dynes/cm 2 and a yield stress of 50 dynes/cm 2 . Both smectics and nematics are viscoelastic solids at very low stress levels, with a modulus that is related to their defect texture. At stress levels somewhat above the yield stress, there is a yielding regime where the deformation rate and defect spacing are power laws in the applied stress. We understand these power laws using the ideas developed long ago by Orowan for the motion of line defects in crystalline solids. The exponents of these power laws are different for nematics and smectics, but the nematic universality class also appears to apply to superplastic metals and ceramics.