  We discuss fluxes of RR and NSNS background fields in type II string
compactifications on non-compact Calabi-Yau threefolds together with their dual
brane description which involves bound states of branes. Simultaneously turning
on RR and NSNS 2-form fluxes in an 1/2 supersymmetric way can be geometrically
described in M-theory by a SL(2,Z) family of metrics of G(2) holonomy. On the
other hand, if the flux configuration only preserves 1/4 of supersymmetries, we
postulate the existence of a new eight-dimensional manifold with spin(7)
holonomy, which does not seem to fit into the classes of known examples. The
latter situation is dual to a 1/4 supersymmetric web of branes on the deformed
conifold. In addition to the 2-form fluxes, we also present some considerations
on type IIA NSNS 4-form and 6-form fluxes.
