  The non-perturbative equivalence of four-dimensional N=2 superstrings with
three vector multiplets and four hypermultiplets is analysed. These models are
obtained through freely acting orbifold compactifications from the heterotic,
the symmetric and the asymmetric type II strings. The heterotic scalar
manifolds are (SU(1,1) / U(1))^3 for the S,T,U moduli sitting in the vector
multiplets and SO(4,4)/ (SO(4) X SO(4)) for those in the hypermultiplets. The
type II symmetric duals correspond to a self-mirror Calabi-Yau threefold
compactification with Hodge numbers h(1,1)=h(2,1)=3, while the type II
asymmetric construction corresponds to a spontaneous breaking of the N=(4,4)
supersymmetry to N=(2,0). Both have already been considered in the literature.
The heterotic construction instead is new and we show that there is a
weak/strong coupling S-duality relation between the heterotic and the
asymmetric type IIA ground state with S(Het)=-1/S(As); we also show that there
is a partial restoration of N=8 supersymmetry in the heterotic strong-coupling
regime. We compute the full (non-)perturbative R2 and F2 corrections and
determine the prepotential.
