The transient response of two thermotropic liquid crystalline polymers (a copolyester of 60 mol %p‐hydroxybenzoic acid, PHB, and 40 mol % poly(ethylene terephthalate), PET, and a copolyester of PHB and 2‐hydroxy‐6‐naphthoic acid, following step strains up to 20 strain units was measured. The relaxation curves typically show an initially rapid decay followed by a long relaxation tail. The lower the temperature, the more remarkable is the length of the long relaxation tail. This behavior makes the LCP uniquely different from most flexible chain polymers such as PET and polystyrene, which show a relaxation modulus which decreases continuously having no discontinuity in the slope. This behavior is probably due to unmelted solid phase which exists in the melt up to quite high temperatures. When the LCP’s are heated to temperatures well above their melting points as determined by DSC, then the long relaxation tails are eliminated. Furthermore, on cooling the sample rapidly down from a temperature well above the melting point the relaxation modulus resembles that at the higher temperature as a result of the supercooling effect. The relaxation modulus was also determined for samples subjected to lubricated squeezing flow. Whereas for polystyrene the relaxation modulus determined in lubricated squeezing flow was equal to that determined in step shear strain experiments, this was not the case for the LCP’s. It is not known whether the behavior reported here is common to nematic LCP’s or to the multiphase structure (crystallites, nematic phase, isotropic phase) which might be present.