  In this paper we study the linear stability of the relative equilibria for
homogeneous and quasihomogeneous potentials. Firstly, in the case the potential
is a homogeneous function of degree $-a$, we find that any relative equilibrium
of the $n$-body problem with $a>2$ is spectrally unstable. We also find a
similar condition in the quasihomogeneous case. Then we consider the case of
three bodies and we study the stability of the equilateral triangle relative
equilibria. In the case of homogeneous potentials we recover the classical
result obtained by Routh in a simpler way. In the case of quasihomogeneous
potentials we find a generalization of Routh inequality and we show that, for
certain values of the masses, the stability of the relative equilibria depends
on the size of the configuration.
