  We study the possibility that the vacuum energy density of scalar and
internal-space gauge fields arising from the process of dimensional reduction
of higher dimensional gravity theories plays the role of quintessence. We show
that, for the multidimensional Einstein-Yang-Mills system compactified on a $R
\times S^3 \times S^d$ topology, there are classically stable solutions such
that the observed accelerated expansion of the Universe at present can be
accounted for without upsetting structure formation scenarios or violating
observational bounds on the vacuum energy density.
