Low molecular weight polystyrene-bloch-polyisoprene (SI diblock) copolymers having a wide range of compositions were synthesized via anionic polymerization, and the order-disorder transition temperatures (T-ODT) of the block copolymers were determined using dynamic viscoelastic measurements. We have shown that logarithmic plots of dynamic storage modulus (G’) versus dynamic loss modulus (G") are very effective to determine the T-ODTS of the block copolymers. The experimentally determined T-ODTS are compared with the predictions made from currently held theories. We point out that the reliability of the predicted T-ODT Of a block copolymer depends, among many factors, on the accuracy of the expression for the Flory-Huggins interaction parameter chi. We observed that the SI diblock copolymers having a low volume fraction of polystyrene or polyisoprene block (e.g., less than about 0.2) exhibited "liquidlike" theological behavior at temperatures below their T-ODTS, for instance at temperatures as low as about 30 degrees C below the T-ODT. We attribute this observation to the existence of defects in the long-range spatial order of microdomains (grain-boundary defects) which are continuous in three-dimensional space. Using the Onuki analysis that the extent of composition fluctuations of a block copolymer near the critical temperature, at a given temperature difference Delta T = T - T-c from the critical temperature T-c, is determined very much by the temperature dependence of the Flory-Huggins interaction parameter chi, we have shown that the extent of composition fluctuations for SI diblock copolymers in the disordered state near the critical temperature is very small. Specifically, we have shown that for the same extent of composition fluctuations epsilon, defined by epsilon = 2 (1 - chi/chi(c)), where chi(c) is the value of chi at the critical point, a temperature difference Delta T of 1 degrees C for an SI diblock copolymer corresponds to ca. 20 degrees C for a 1,2-polybutadiene-block-1,4-polybutadien copolymer. This difference in Delta T between the two block copolymer systems is attributed to the difference in the temperature coefficient B appearing in the expression, chi = A + B/T. Using the Onuki analysis, we have shown further that the extent of composition fluctuations in the disordered state near the critical temperature varies little with block copolymer composition.