  We analyse a class of four-dimensional heterotic ground states with N=2
space-time supersymmetry. From the ten-dimensional perspective, such models can
be viewed as compactifications on a six-dimensional manifold with SU(2)
holonomy, which is locally but not globally K3 x T^2. The maximal N=4
supersymmetry is spontaneously broken to N=2. The masses of the two massive
gravitinos depend on the (T,U) moduli of T^2. We evaluate the one-loop
threshold corrections of gauge and R^2 couplings and we show that they fall in
several universality classes, in contrast to what happens in usual K3 x T^2
compactifications, where the N=4 supersymmetry is explicitly broken to N=2, and
where a single universality class appears. These universality properties follow
from the structure of the elliptic genus. The behaviour of the threshold
corrections as functions of the moduli is analysed in detail: it is singular
across several rational lines of the T^2 moduli because of the appearance of
extra massless states, and suffers only from logarithmic singularities at large
radii. These features differ substantially from the ordinary K3 x T^2
compactifications, thereby reflecting the existence of spontaneously-broken N=4
supersymmetry. Although our results are valid in the general framework defined
above, we also point out several properties, specific to orbifold
constructions, which might be of phenomenological relevance.
