The limit of validity of the slowly varying envelope approximation (SVEA) is derived as a function of the “bulk” velocity v of the radiating system, which reads l p λ(1− v/c ), l p being the radiation pulse length. This condition reduces to the usual SVEA in the limit v/c 1, whereas it is sensibly relaxed in the relativistic limit. The relevance for the case of microwave free electron lasers is discussed.