Let E be an infinite set of cardinality m, and let P E be the set of all functions defined on E. We prove that the cardinality of the family of all classes precomplete in P E is equal to $$2^{2^m }$$ . If C ℝ is the set of all continuous functions of real variables, then the cardinality of the family of all classes precomplete in C ℝ is equal to $$2^{2^{\aleph _0 } }$$ .