Shear viscosities and oscillatory viscosities were measured for the two-phase system polyethylene oxide/poly(dimethylsiloxane) at 70 degrees C as a function of composition. This blend exhibits the usual droplet/matrix structures in the vicinity of the pure components and a region of co-continuity within which two droplet/matrix structures coexist. A stepwise reduction in the shear rate,gamma, leads to a rapid increase in viscosity followed by a much slower exponential decay; plots of the corresponding rate constants as a function of composition exhibit two discontinuities marking the boundaries of co-continuity; a similar dependence is obtained for the time independent final viscosities eta(infinity). Keeping the blend composition constant and determining eta(infinity) as a function of gamma yields a curve that passes a distinct maximum, where the viscosities are very close to that of the less viscous pure component on both ends of this dependence. The dynamic mechanical measurements of the blends yield at low frequencies storage moduli G' that are orders of magnitude larger than that of the components because of the deformation of the interfaces. At high frequencies, the loss moduli G '' reflect the increasing alignment of the drops suspended in the matrix phases. The composition dependencies of G' and of the complex viscosities can again be used to determine the limits of co-continuity.