  We construct supergravity solutions describing branes (D2-branes or
NS5-branes or waves) localized within D6-branes in the region close to the core
of the D6-branes. Other similar string-theory and M-theory `near-core'
localized solutions can be found by applying U-duality and/or lifting D=10
solutions to D=11. In particular, the D2-branes localized on D6-branes is
T-dual to a special case of the background describing (D)strings localized on
(D)5-branes and thus is also related to a localized intersection of M2-branes
and M5-branes. D6+wave configuration is U-dual to a D0-brane localized on a
Kaluza-Klein 5-brane or to the fundamental string intersecting a D5-brane with
the point of intersection localized on the D5-brane.
