We first review the problem of superluminal propagation or even loss of propagation for higher spin fields minimally coupled to an external electromagnetic field, discovered by Velo and Zwanziger in the 1960's. Then, we show that these fields have a nonlocal structure. This indicates that these fields have internal structure and should not be considered as elementary. The main tool in this investigation is the use of a Peirce decomposition of the algebra of the matrices occuring in the first order wave equations for these fields.