  We introduce global wave-front sets $\operatorname{WF}_{{\mathcal B}} (f)$,
$f\in {\mathscr S}^\prime(\textbf{R}^d)$, with respect to suitable Banach or
Fr\'echet spaces ${\mathcal B}$. An important special case is given by the
modulation spaces ${\mathcal B}=M(\omega,\mathscr B)$, where $\omega$ is an
appropriate weight function and $\mathscr B$ is a translation invariant Banach
function space. We show that the standard properties for known notions of
wave-front set extend to $\operatorname{WF}_{{\mathcal B}} (f)$. In particular,
we prove that micro locality and microellipticity hold for a class of globally
defined pseudo-differential operators $\operatorname{Op}_t(a)$, acting
continuously on the involved spaces.
