Let (X, d) be a metric space and let Lip(X, d) denote the complex algebra of all complex-valued bounded functions f on X for which f is a Lipschitz function on (X, d). In this paper we give a complete description of all 2-local real and complex uniform isometries between Lip(X, d) and Lip(Y, ρ), where (X, d) and (Y, ρ) are compact metric spaces. In particular,we showthat every 2-local real (complex, respectively) uniform isometry from Lip(X, d) to Lip(Y,ρ) is a surjective real (complex, respectively) linear uniform isometry. e
