The invention relates to flame-retardant cellulosic man-made fibers containing a flame-retardant substance in the form of an oxidized condensate of a tetrakis hydroxyalkyl phosphonium salt with ammonia and/or a nitrogenous compound which contains one or several amine groups whereby the fiber has a tenacity of more than 18 cN/tex in a conditioned state. Production process and the use of the fibers according to the invention are further objects of the invention.