  We have examined the deformation of a generic non-Abelian gauge theory
obtained by replacing its Lie group by the corresponding quantum group. This
deformed gauge theory has more degrees of freedom than the theory from which it
is derived. By going over from point particles in the standard theory to
solitonic particles in the deformed theory, it is proposed to interpret the new
degrees of fredom as descriptive of a non-locality of the deformed theory. It
also turns out that the original Lie algebra gets replaced by two dual
algebras, one of which lies close to and approaches the original Lie algebra in
a correspondence limit, while the second algebra is new and disappears in this
same correspondence limit. The exotic field particles associated with the
second algebra can be interpreted as quark-like constituents of the solitons,
which are themselves described as point particles in the first algebra. These
ideas are explored for q-deformed SU(2) and $GL_q(3)$.
