Blends of 1,4-polybutadiene (7% 1,2) and 1,2-polybutadiene (63% 1,2) have been studied. The molecular weights are sufficiently high that the polymers are in the entanglement regime (5-20 entanglements per chain). DSC studies confirm that the blends are miscible. A single glass transition is observed, intermediate between the glass transition temperatures of the homopolymers. The T(g) of the blends is however 2-3 times wider than that in the homopolymers. The viscoelastic properties of the blends have been studied over a wide range of temperatures and frequencies. The blends appear to be thermorheologically complex. This is a consequence of different temperature dependences of the relaxation times of the components of the blends. Analysis of these temperature dependences suggests that each component experiences its own T(g), slightly different from the average DSC T(g). These different T(g)'s suggest that each polymer is preferentially surrounded by its own chains. Other consequences of thermorheological complexity are also described.