We have studied the oscillatory shear response of three thermotropic s
mectic-A liquid crystalline materials with no external aligning field
(other than the necessary presence of rheometer plates). Two are polym
ers (one main-chain and one side-chain) and the other is a small molec
ule smectic. All three exhibit the classical linear response to oscill
atory shear characteristic of a viscoelastic solid at sufficiently sma
ll strain amplitudes and frequencies. However, for strain amplitudes e
xceeding a small critical value, these materials exhibit a strongly no
nlinear response to strain, which is characterized in detail. While th
e low-strain moduli and the critical strain of the three smectics are
considerably different, the nonlinear response has some universal char
acter which is presumably related to the low energy for the formation
of defects in smectic liquid crystals.