Functions defined on closed subsets of elliptic curves equation presented are considered. The following converse theorem of approximation is established. Consider a function f : G → C. Assume that there is a sequence of polynomials P_n(ζ, w) in two variables, deg P_n ≤ n, such that the following inequalities are valid: equation presented where 0 < α < 1. Then the function f necessarily belongs to the class H ^α(G). The direct approximation theorem was proved in the previous paper by the authors. Thus, a constructive description of the class H^α(G) is obtained. Bibliography: 6 titles.