  The nonextensive statistics based on Tsallis entropy have been so far used
for the systems composed of subsystems having same $q$. The applicability of
this statistics to the systems with different $q$'s is still a matter of
investigation. The actual difficulty is that the class of systems to which the
theory has been applied is limited by the usual nonadditivity rule of Tsallis
entropy which, in reality, has been established for the systems having same $q$
value. In this paper, we propose a more general nonadditivity rule for Tsallis
entropy. This rule, as the usual one for same $q$-systems, can be proved to
lead uniquely to Tsallis entropy in the context of systems containing different
$q$-subsystems. A zeroth law of thermodynamics is established between different
$q$-systems on the basis of this new nonadditivity.
