Two dielectric relaxations, βsp (1.5MHz) and γ1sp (7MHz), have been detected on spectrin-based membrane skeleton (MS) of red blood cells (RBCs) using the plot of admittance changes at the spectrin denaturation temperature (Ivanov and Paarvanova in Bioelectrochemistry 110: 59-68, 2016, Electrochim Acta 317: 289-300, 2019a). In this study, we treated RBCs and RBC ghost membranes with agents that make membranes rigid and suppress membrane flicker, and studied the effect on βsp and γ1sp relaxations. Diamide (diazene dicarboxylic acid bis-(N,N-dimethylamide)) (up to 0.85mM), taurine mustard (tris(2-chloroethyl)amine) (up to 2mM), known to specifically cross-link and stiffen spectrin, and glutaraldehyde (up to 0.044%) all inhibited the relaxations in RBC ghost membranes. Similar inhibition was obtained resealing RBC ghost membranes with 2,3-diphosphoglicerate (up to 15mM), binding WGA (wheat germ agglutinin) (up to 0.025mg/ml) to exofacial aspect of RBCs, incubating RBCs in hypotonic (200mOsm) and hypertonic (600-900mOsm) media and depleting RBCs of ATP. By contrast, concanavalin A (1mg/ml) and DIDS (4,4'-diiso-thiocyanato stilbene-2,2'-disulfonic acid) (75μM, pH 8.2), both known to bind specifically band 3 integral protein of RBCs without effect on RBC membrane rigidity, did not affect the relaxations. We conclude there might be a relation between the strength of dielectric relaxations on MS spectrin and the deformability and flicker of RBC membrane.