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We explore effects of the Shakura-Sunyaev alpha-viscosity on the dynamics and oscillations of slender tori. We start with a slow secular evolution of the torus. We show that the angular-momentum profile approaches the Keplerian one on a timescale longerthan a dynamical one by a factor on the order of 1/alpha. We then focus our attention on the oscillations of the torus. We discuss the effects of various angular-momentum distributions. Using a perturbation theory, we have found a rather general result that the high-order acoustic modes are damped by the viscosity, while the high-order inertial modes are enhanced. We calculate viscous growth rates for the lowest-order modes, and show that already the lowest-order inertial mode is unstable for less-steepangular-momentum profiles, or very close to the central gravitating object.