  We represent a new microscopic approach that allows studying the propagation
properties of microwaves in a Bose-Einstein condensate of alkali atoms. It is
assumed that the frequency of signal is tuned up to the transition between
hyperfine ground state levels of such atoms. Pulse slowing conditions
dependence on the system parameters is found. It is shown that the slowed
signal can propagate in mentioned system with rather small energy loss. Such
phenomenon is also studied in case of hyperfine levels Zeeman splitting. A
possibility of ultra-slow microwaves observing in a condensed gas of cesium
atoms is discussed.
