We give all the meromorphic functions defined near the origin 0 e C satisfying a functional equation investigated by Bruschi and Calogero [1], [2]. § 0. Introduction It is an important problem to find a Lax pair L and M whose equations of motion are equivalent to the Lax equation [10], [11], [12]. In order to prove their complete integrability it is convenient to use a Lax representation.The systems of Calogero-Sutherland type, which describe one-dimensional n-particle dynamics, are defined by the following Hamiltonian where the potential U has the form Communicated by T. Kawai, July 8, 1999. Revised November 1, 1999. 1991 Here a(jx\ r lf r z ) fs JAe Wefersfross segrafl function, and £(x\ r lf r 2 ) £/z# Weierstrass zeta function. All the solutions except for the case (0-i) extend themselves to meromorphic functions defined on the whole plane C .It should be remarked that a meromorphic function defined near the origin 0 EE C is holomorphic on a sufficiently small punctured disk. Hence our result covers all the meromorphic solutions defined near the origin 0 e C .The methods we use in this paper are quite different from those of Bruschi and Calogero [1], [2].The outline to get all meromorphic solutions is as follows. First, we shall show that the solution 77 is the logarithmic derivative of some meromorphic function