We describe a class of diffeomorphism-invariant SU( N) gauge theories in dimensions, together with some matter couplings. These theories have local degrees of freedom, and have the unusual feature that the constraint associated with time reparametrizations is identically satisfied. A related class of SU( N) theories in dimensions has the constraint algebra of general relativity, but has more degrees of freedom. Non-perturbative quantization of the first type of theory via SU( N) spin networks is briefly outlined.