Nevanlinna Matrices of Entire Functions

The notion of a pre-Nevanlinna matrix of entire functions is introduced, and we find necessary and sufficient conditions for an entire function to belong to such a matrix, thereby generalizing previous work of Krein. If one of the functions in a pre-Nevanlinna matrix is a polynomial, then the three others arc also polynomials and their degrees differ by at most two. If the functions in a pre-Nevanlinna matrix are transcendental they have necessarily the same order, type and indicators.