  We examine non-gravitational minimal supermultiplets which are based on the
tensor gauge fields appearing as matter fields in exceptional generalised
geometry. When possible, off-shell multiplets are given. The fields in the
multiplets describe non-gravitational parts of the internal dynamics of
compactifications of M-theory. In flat backgrounds, they enjoy a global
U-duality symmetry, but also provide multiplets with a possibility of coupling
to a generalised exceptional geometry.
