We construct a general class of chiral four-dimensional string models with Scherk-Schwarz supersymmetry breaking, involving freely acting orbifolds. The basic ingredient is to combine an ordinary supersymmetry-preserving Z(N) projection with a supersymmetry-breaking projection Z'(M) acting freely on a subspace of the internal manifold. A crucial condition is that any generator of the full orbifold group Z(N)xZ'(M) must either preserve some supersymmetry or act freely in order to become irrelevant in some large volume limit. Tachyons are found to be absent or limited to a given region of the tree-level moduli space. We find several new models with orthogonal supersymmetries preserved at distinct fixed-points. Particular attention is devoted to an interesting Z(3)xZ'(3) heterotic example.