In order to pass through the microcirculation, red blood cells (RBCs) need to undergo extensive deformations and to recover the original shape. This extreme deformability is altered by various pathological conditions. On the other hand, an altered RBC deformability can have major effects on blood flow and can lead to pathological implications. The study of the viscoelastic response of red blood cells to mechanical stimuli is crucial to fully understand deformability changes under pathological conditions. However, the typical erythrocyte biconcave shape hints to a complex and intrinsically heterogeneous mechanical response that must be investigated by using probes at the nanoscale level. In this work, the local viscoelastic behaviour of healthy and pathological red blood cells was probed by Atomic Force Microscopy (AFM). Our results clearly show that the RBC stiffness is not spatially homogeneous, suggesting a strong correlation with the erythrocyte biconcave shape. Moreover, our nanoscale mapping highlights the key role played by viscous forces, demonstrating that RBCs do not behave as pure elastic bodies. The fundamental role played by viscous forces is further strengthened by the comparison between healthy and pathological (diabetes mellitus) RBCs. It is well known that pathological RBCs are usually stiffer than the healthy ones. Our measures unveil a more complex scenario according to which the difference between normal and pathological red blood cells does not merely lie in their stiffness but also in a different dynamical response to external stimuli that is governed by viscous forces.