Although human red blood cell (RBC) suspensions exhibit viscoelastic behavior, the relations between this behavior and the viscoelastic properties of individual RBC are not well defined. Using an oscillatory Couette viscometer (oscillatory frequency 0.01 to 1.0 Hz, amplitude ±1°), we have measured the viscous (η′) and elastic (η″) components of the complex viscosity at 25°C for cells suspended in buffer at 80% hematocrit. Control RBC were compared to cells which had known alterations in their viscoelastic properties: (1) heat‐treated cells; (2) age‐separated cells; (3) cells in nonisotonic media (up to approximately 30% volume change). All suspensions exhibited decreases in η′ and η″ with increasing frequency, although the differences between altered cells and controls did not vary strongly with frequency. Suspensions of heat‐treated and maximally shrunk cells showed the greatest changes in viscoelasticity compared to controls: for heat‐treated cells, η′ was raised by 44% on average and η″ was raised by 67%; for maximally shrunk RBC, η′ was raised by 210% and η″ by 160%. Old cells showed slight increases (∼17%) in both components of the complex viscosity, but only minimal changes in viscoelasticity were noted for swollen RBC and young cell suspensions. Use of a Kelvin‐Voigt solid model indicated that the elastic component could not be entirely attributed to the RBC membrane elasticity but that the viscous component was probably dominated by the RBC membrane viscosity; a modified model, incorporating an additional elastic element, allowed the suspension elasticity to be better correlated with the known changes in cellular properties.