The problem of constructing a manifestly covariant field theory for spin-3 fields with interactions is reconsidered using results from the light-cone treatment of higher-spin fields. In the case of self-interactions, structure relations for the gauge algebra are studied. It is shown that the possible field-independent structure relations that could be derived from the gauge transformations given to first order in the coupling constant do not obey the Jacobi identity. Minimal and nonminimal couplings to Yang-Mills fields are also studied. In this case, the gauge covariance of the field equation fails.

• Received 18 October 1983

DOI:https://doi.org/10.1103/PhysRevD.32.2031