LetAbe an artin algebra. An indecomposableA-moduleMis called weakly directing if it does not belong to a cycleof nonzero nonisomorphisms between indecomposable modules from the same component of. This paper deals with weakly directing modules. We investigate the distinctions and connections between weakly directing modules and directing modules. We also show that all weakly directing modules are distributed to finitely many DTr-orbits.