Earlier work on mechanical properties and their relation to phase diagrams is complemented here by rheological and further morphological studies using an optical microscope and polarizing light, for the system studied previously and also for three other binary blend systems. The polymer liquid crystal (PLC) is the same in all, PET/0.6PHB, where PET = poly(ethylene terephthalate), PHB = p-hydroxybenzoic acid and 0.6 = the mole fraction of PHB in the copolymer. The engineering polymers (EPs) used are, in turn, bisphenol-A-polycarbonate (PC), poly(butylene terephthalate) (PET), isotactic polypropylene (PP) and poly(vinylidene fluoride) (PVDF). Blends of concentration up to 20 wt% PET/0.6PHB were studied. In all four binary systems and for all shear rates, the addition of PET/0.6PHB to an EP results in a lowering of the melt viscosity (eta), down to approximately 30% of the value for the respective pure EP. The results are explained in terms of the Wissbrun model of PLC melts; the mechanism of the viscosity lowering is different from that in incompatible blends of flexible polymers. With the exception of PC + PET/0.6PHB blends, a shear rate dependence of the viscosity modification by the PLC is also observed. This difference can be explained by the miscibility of PC with PHB in the PLC as reported earlier, while the remaining three EPs are immiscible with the PLC. The concentration theta(LC limit) at which liquid crystal (LC)-rich islands are formed in the LC-poor matrix is between 15 and 20wt% PLC in the systems studied. An equation for blend viscosity proposed by Borisenkova et al. has been generalized to the form 1n(eta(blend)/eta(matrix)) = a(0) + a(1) 1n(eta(matrix)/eta(PLC)) + a(2) 1n(2)(eta(matrix)/eta(PLC)), where a(0), a(1) and a(2) are parameters for a given class of blends; the type of EP and the shear rate are implicit variables which define eta(matrix)/eta(PLC). The master curve corresponding to that equation exists only for theta greater than or equal to theta(LC limit).