Consistency problems are discussed for models where the electromagnetic field and a neutral vector-meson field are coupled to the same current. It is shown that the conventional formulation of this model is inconsistent if the bare meson mass is infinite. However, no contradiction could be found for a different formulation of the model which is due to Kroll, Lee and Zumino. Finally a simple proof is given that the wave-function renormalization constant of the electromagnetic field is finite in this model.