We present invariant actions describing (1,0) supersymmetric non-abelianleftons and rightons on coset manifolds. Our discussion covers both chiral and non-chiral cases of the (1,0) supersymmetric WZNW actions. We analyze the supergravitational, chiral and Siegel anomalies of D<10 heterotic strings within the lagrangian realization of GKO coset construction. General conditions for anomaly cancellation are found and various anomaly-free solutions are discussed. Among these are the “realistic” ones, such as the Gepner models and the four-dimensional heterotic strings compactified on orbifolds. Coupling of the heterotic string coset models to bosonic massless modes and the Siegel anomalies of the associated non-linear α-models are briefly considered.