The limit of validity of the slowly varying envelope approximation (SV
EA) is derived as a function of the ''bulk'' velocity upsilon of the r
adiating system, which reads l(p) much greater than lambda(1 - upsilon
/c), l(p) being the radiation pulse length. This condition reduces to
the usual SVEA in the limit upsilon/c much less than 1, whereas it is
sensibly relaxed in the relativistic limit. The relevance for the case
of microwave free electron lasers