  The paper is devoted to the development of new sufficient conditions for the
calmness and the Aubin property of implicit multifunctions. As the basic tool
one employs the directional limiting coderivative which, together with the
graphical derivative, enable us a fine analysis of the local behavior of the
investigated multifunction along relevant directions. For verification of the
calmness property, in addition, a new condition has been discovered which
parallels the missing implicit function paradigm and permits us to replace the
original multifunction by a substantially simpler one. Moreover, as an
auxiliary tool, a handy formula for the computation of the directional limiting
coderivative of the normal-cone map with a polyhedral set has been derived
which perfectly matches the framework of [11]. All important statements are
illustrated by examples.
