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We investigate the stability of Fredholm properties on interpolation scales of quasi-Banach spaces. This analysis is motivated by problems arising in PDE's and several applications are presented. Interpolation scales of quasi-Banach spaces. The abstract setup Throughout the paper, for a quasi-normed space (X, · X ), we shall denote by ρ = ρ(X) its modulus of concavity, i.e. the smallest positive constant for which x,y∈X (note that always ρ(X) ≥ 1). We recall the Aoki-Rolewicz theorem , doi:10.1090/s0002-9947-98-02008-x fatcat:v6pd2jzi4bggdp366xkiwxfspa