The aim of this paper is to study some brackets defined on (τ,σ)-derivations satisfying quasi-Lie identities. Moreover, we provide examples of (p, q)-deformations of Witt and Virasoro algebras as well as sl(2) algebra. These constructions generalize the results obtained by Hartwig, Larsson and Silvestrov on σ-derivations, arising in connection with discretizations and deformations of algebras of vector fields.