Discovered effectively two decades ago, the ''rotospheres'' (or also t
he regions ''in a pre-horizon regime'') around collapsed relativistic
sources have been analyzed thoroughly (and given their name) just late
ly. So far only those specified by the unusual behaviour of accelerati
on of the observer in azimuthal motion have been considered. Here I fi
nd, in Kerr spacetimes, the rotospheres defined with respect to latitu
dinal motion.