The dynamics and deformation of red blood cells (RBCs) in microcirculation affect the flow resistance and transport properties of whole blood. One of the key properties that can alter RBC dynamics in flow is the contrast λ (or ratio) of viscosities between RBC cytosol and blood plasma. Here, we study the dependence of RBC shape and dynamics on the viscosity contrast in tube flow, using mesoscopic hydrodynamics simulations. State diagrams of different RBC dynamical states, including tumbling cells, parachutes, and tank-treading slippers, are constructed for various viscosity contrasts and wide ranges of flow rates and tube diameters (or RBC confinements). Despite similarities in the classification of RBC behavior for different viscosity contrasts, there are notable differences in the corresponding state diagrams. In particular, the region of parachutes is significantly larger for λ = 1 in comparison to λ = 5. Furthermore, the viscosity contrast strongly affects the tumbling-to-slipper transition, thus modifying the regions of occurrence of these states as a function of flow rate and RBC confinement. Also, an increase in cytosol viscosity leads to a reduction in membrane tension induced by flow stresses. Physical mechanisms that determine these differences in RBC dynamical states as a function of λ are discussed. © Copyright © 2021 Dasanna, Mauer, Gompper and Fedosov.