The morphology and melt rheological properties were characterized for a polymer blend where the viscosity ratio was changing with time. The reactive phase, an ethylene methyl acrylate (EMA) copolymer containing a diol, was blended in the melt with linear low density polyethylene (LLDPE). Dual continuity was found for the initial morphology of the reactive blends over a broad range of composition in contradiction with the phase inversion rule : Phi(A) eta(B) = Phi(B) eta(A). The influence of blending conditions and annealing on the initial morphology was studied. For a blend where the LLDPE phase is initially dispersed in EMA, the torque and normal force measured in the parallel plate geometry go through a maximum when the morphology becomes co-continuous.