Small amplitude oscillatory shear has been used to study thermotropic liquid-crystalline polymers that have mesogenic groups pendant to flexible backbones. The polymers studied form nematic and smectic glasses, enabling viscoelastic response to be studied over a wide range of frequencies using time-temperature superposition. In contrast to main chain liquid-crystalline polymers, the nematic side chain polymers exhibit linear viscoelastic response over a wide range of strain amplitudes that is independent of thermal and shear histories. Viscoelastic response is very sensitive to smectic-nematic and smectic-isotropic transitions, but insensitive to the nematic-isotropic transition, as time-temperature superposition applies across this transition. We compare viscoelastic data with diffusion data by calculating the time τ that it takes a polymer to diffuse a distance equal to its coil sizeR(τ=R2/D). At frequencies lower than 1/τ side chain polymers in their nematic show the terminal response characteristic of viscoelastic liquids. In their smectic, they are still strongly viscoelastic at frequencies lower than 1/τ and approach the terminal response of a viscoelastic solid at the lowest frequencies. Implications of such behaviour are discussed.