We have studied the dynamic and theological properties in the single-phase channels of a microemulsion system with a mixed anionic/nonionic surfactant system and decane from the aqueous to the oil phase. One isotropic channel, called the "upper" channel, begins at the L(3) phase (sponge-like phase) of the binary surfactant mixture on the water side and passes with a shallow minimum for the surfactant composition to the oil side. The other "lower" single-phase channel begins at the micellar L(1) phase and ends in the middle of the phase diagram. Both isotropic channels are separated by a huge anisotropic single phase L(alpha) channel that reaches from the water side to 90% of oil in the solvent mixture. The structural relaxation time of the viscous fluids could be measured with electric birefringence (EB) measurements, where a signal is caused by the deformation of the internal nanostructure of the fluids by an electric field. For the L(3) phase, the EB signal can be fitted with a single time constant. With increasing oil in the upper channel, the main structural relaxation time passes over a maximum and correlates with the viscosity. Obviously, this time constant controls the viscosity of the fluid (eta degrees = G'.tau). It is remarkable that the longest structural relaxation time increases three decades, and the viscosity increases two decades when 10% of oil is solubilized into the L(3) phase. Conductivity data imply that the fluid in the upper channel has a bicontinuous structure from the L(3) phase to the microemulsion with only 10% oil. In this oil range, the conductivity decreases three decades, and the electric birefringence signals are complicated because of a superposition of up to three processes. For higher oil ratios, the structure obviously changes to a HIPE (high internal phase emulsion) structure with water droplets in the oil matrix.