  We study the properties of {\bf exact} (all level $k$) quantum coherent
states in the context of string theory on a group manifold (WZWN models).
Coherent states of WZWN models may help to solve the unitarity problem: Having
positive norm, they consistently describe the very massive string states
(otherwise excluded by the spin-level condition). These states can be
constructed by (at least) two alternative procedures: (i) as the exponential of
the creation operator on the ground state, and (ii) as eigenstates of the
annhilation operator. In the $k\to\infty$ limit, all the known properties of
ordinary coherent states are recovered. States (i) and (ii) (which are
equivalent in the context of ordinary quantum mechanics and string theory in
flat spacetime) are not equivalent in the context of WZWN models. The set (i)
was constructed by these authors in a previous article. In this paper we
provide the construction of states (ii), we compare the two sets and discuss
their properties. We analyze the uncertainty relation, and show that states
(ii) satisfy automatically the {\it minimal uncertainty} condition for any $k$;
they are thus {\it quasiclassical}, in some sense more classical than states
(i) which only satisfy it in the $k\to\infty$ limit. Modification to the
Heisenberg relation is given by $2 {\cal H}/k$, where ${\cal H}$ is connected
to the string energy.
