  We define a very general class of CHL-models associated with any string
theory (bosonic or supersymmetric) compactified on an internal CFT C x T^d. We
take the orbifold by a pair (g,\delta), where g is a (possibly non-geometric)
symmetry of C and \delta is a translation along T^d. We analyze the T-dualities
of these models and show that in general they contain Atkin-Lehner type
symmetries. This generalizes our previous work on N=4 CHL-models based on
heterotic string theory on T^6 or type II on K3 x T^2, as well as the
`monstrous' CHL-models based on a compactification of heterotic string theory
on the Frenkel-Lepowsky-Meurman CFT V^{\natural}.
