  We consider $n$-body problems given by potentials of the form ${\alpha\over
r^a}+{\beta\over r^b}$ with $a,b,\alpha,\beta$ constants, $0\le a<b$. To
analyze the dynamics of the problem, we first prove some properties related to
central configurations, including a generalization of Moulton's theorem. Then
we obtain several qualitative properties for collision and near-collision
orbits in the Manev-type case $a=1$. At the end we point out some new
relationships between central configurations, relative equilibria, and
homothetic solutions.
