  We study the composition of time-ffrequency localization operators
(wavepacket operators) and develop a symbolic calculus of such operators on
modulation spaces. The use of time-frequency methods (phase space methods)
allows the use of rough symbols of ultra-rapid growth in place of smooth
symbols in the standard classes. As the main application it is shown that, in
general, a localization operators possesses the Fredholm property, and thus its
range is closed in the target space.
