Viscosity, mu, of Ugnu heavy oil (North Slope of Alaska, USA) saturated with methane was measured at temperatures from 0 to 60 degrees C, pressure from 15 to 1800 psi, and shear rate of 0.1-500 s(-1) using a high-pressure rheology apparatus constructed for this work. Under all saturated conditions, the oil behaves as a Newtonian fluid. The influence of temperature, pressure, and methane concentration was analyzed, and important regularities in the viscosity were established. A two-variable Antoine-type correlation, mu = f(T, p), with 6 fitting parameters was developed using 48 points on a p,T,mu-diagram for Ugnu oil. Since produced oil is accompanied by sand and water, their influence on the viscosity of Ugnu oil saturated with methane at 1500 psi was also studied. The relative viscosity of the Ugnu oil + water emulsions at temperatures from 2 to 60 degrees C increased linearly with increasing water concentration from 0 to 20 wt % following the Einstein viscosity model for dilute suspensions. Although possible in the time scale of days, hydrate formation at temperatures below 13 degrees C (thermodynamic hydrate formation temperature at 1500 psi) did not interfere with the rheological measurements for the emulsions. Due to rapid sand particle sedimentation in methane-saturated Ugnu oil during experimental stages, the impact of sand concentration on the live oil viscosity could not be evaluated. Overall, the viscosity of Ugnu oil as a function of pressure and temperature can be used to simulate the oil's behavior during production.