  We consider four dimensional CHL models with sixteen spacetime
supersymmetries obtained from orbifolds of type IIA superstring on K3 x T^2 by
a Z_N symmetry acting (possibly) non-geometrically on K3. We show that most of
these models (in particular, for geometric symmetries) are self-dual under a
weak-strong duality acting on the heterotic axio-dilaton modulus S by a "Fricke
involution" S --> -1/NS. This is a novel symmetry of CHL models that lies
outside of the standard SL(2,Z)-symmetry of the parent theory, heterotic
strings on T^6. For self-dual models this implies that the lattice of purely
electric charges is N-modular, i.e. isometric to its dual up to a rescaling of
its quadratic form by N. We verify this prediction by determining the lattices
of electric and magnetic charges in all relevant examples. We also calculate
certain BPS-saturated couplings and verify that they are invariant under the
Fricke S-duality. For CHL models that are not self-dual, the strong coupling
limit is dual to type IIA compactified on T^6/Z_N, for some Z_N-symmetry
preserving half of the spacetime supersymmetries.

High Energy Physics - Theory;Number Theory