  We define $N_\infty$-operads in the globally equivariant setting and
completely classify them. These global $N_\infty$-operads model intermediate
levels of equivariant commutativity in the global world, i. e. in the setting
where objects have compatible actions by all compact Lie groups. We classify
global $N_\infty$-operads by giving an equivalence between the homotopy
category of global $N_\infty$-operads and the partially ordered set of global
transfer systems, which are much simpler, algebraic objects. We also explore
the relation between global $N_\infty$-operads and $N_\infty$-operads for a
single group, recently introduced by Blumberg and Hill. One interesting
consequence of our results is the fact that not all equivariant
$N_\infty$-operads can appear as restrictions of global $N_\infty$-operads.
