  The integrability of a classical Calogero systems with anti-periodic boundary
condition is studied. This system is equivalent to the periodic model in the
presence of a magnetic field. Gauge momentum operators for the anti-periodic
Calogero system are constructed. These operators are hermitian and
simultaneously diagonalizable with the Hamiltonian. A general scheme for
constructing such momentum operators for trigonometric and hyperbolic
Calogero-Sutherland model is proposed. The scheme is applicable for both
periodic and anti-periodic boundary conditions. The existence of these momentum
operators ensures the integrability of the system. The interaction parameter
$\lambda$ is restricted to a certain subset of real numbers. This restriction
is in fact essential for the construction of the hermitian gauge momentum
operators.
