A series of polydimethylsiloxane based multiblock[AB]ncopolymers was prepared and characterized. The hard blocks included poly(aryl ethers), poly(aryl esters), poly(aryl carbonates), a poly(cycloaliphatic carbonate), polystyrene, and poly(α‐methylsytrene). All of these materials could be solution cast into films which had attractive physical properties and which displayed two‐phase behavior. However, their rheological characteristics (in particular their melt processibility) were found to differ dramatically when the chemical structure of the hard block was varied. Thus, the polysulfone‐polydimethylsiloxane block copolymer could not even be satisfactorily compression molded owing to its inordinately high melt viscosity and melt elasticity. On the other hand, the copolymer prepared from the polycarbonate of 2,2,4,4‐tetramethyl‐1,3‐cyclobutanediol could be readily molded and extruded. The behavior is believed to be related to the retention of a physical network at temperatures well above the upper glass transition. Available data are in agreement with this interpretation. It is proposed that processibility characteristics of block copolymers are related to the intersegment solubility parameter differential, Δ. Our preliminary results suggest that an optimum balance of engineering properties and processibility in two‐phase block or graft copolymers should be observed when the value of Δ is approximately unity. For crystallizable systems, the Δ value in the polymer melt should be essentially zero, if one or both of the segments can subsequently crystallize and hence induce microphase separation.