  Let $C$ be a hyperelliptic curve of genus $g>1$ over an algebraically closed
field $K$ of characteristic zero and $O$ one of the $(2g+2)$ Weierstrass points
in $C(K)$. Let $J$ be the jacobian of $C$, which is a $g$-dimensional abelian
variety over $K$. Let us consider the canonical embedding of $C$ into $J$ that
sends $O$ to the zero of the group law on $J$. This embedding allows us to
identify $C(K)$ with a certain subset of the commutative group $J(K)$.
  A special case of the famous theorem of Raynaud (Manin--Mumford conjecture)
asserts that the set of torsion points in $C(K)$ is finite. It is well known
that the points of order 2 in $C(K)$ are exactly the "remaining" $(2g+1)$
Weierstrass points. One of the authors proved that there are no torsion points
of order $n$ in $C(K)$ if $3\le n\le 2g$. So, it is natural to study torsion
points of order $2g+1$ (notice that the number of such points in $C(K)$ is
always even). Recently, the authors proved that there are infinitely many (for
a given $g$) mutually nonisomorphic pairs $C,O)$ such that $C(K)$ contains at
least four points of order $2g+1$.
  In the present paper we prove that (for a given $g$) there are at most
finitely many (up to a isomorphism) pairs $(C,O)$ such that $C(K)$ contains at
least six points of order $2g+1$.
