Given m rational functions f i ( X 1, …, X n ) (1 ≤ i ≤ m), in n variables, with coefficients in a number field K. The Diophantine problem discussed is as follows: under what conditions does there exist a vector ( z 1, …, z n ) of numbers algebraic over K, such that the f i ( z 1, …, z n ) are algebraic integers? This is called a Skolem problem with data f 1, …, f m . In this paper a Hasse principle (local-global) for Skolem problems is established. This result implies that there exists a decision procedure for Skolem problems, because the corresponding local problems are decidable due to A. Robinson. Parallel to the Hasse principle, a strong approximation theorem is proved, which says that the space of global solutions of a Skolem problem is dense in the space of adelic solutions.