  We construct six-dimensional (1,0) superconformal models with non-abelian
gauge couplings for multiple tensor multiplets. A crucial ingredient in the
construction is the introduction of three-form gauge potentials which
communicate degrees of freedom between the tensor multiplets and the Yang-Mills
multiplet, but do not introduce additional degrees of freedom. Generically
these models provide only equations of motions. For a subclass also a
Lagrangian formulation exists, however it appears to exhibit indefinite metrics
in the kinetic sector. We discuss several examples and analyze the excitation
spectra in their supersymmetric vacua. In general, the models are
perturbatively defined only in the spontaneously broken phase with the vev of
the tensor multiplet scalars serving as the inverse coupling constants of the
Yang-Mills multiplet. We briefly discuss the inclusion of hypermultiplets which
complete the field content to that of superconformal (2,0) theories.
