  We consider the $n$--body problem defined on surfaces of constant negative
curvature. For the case of $n$--equal masses we prove that the hyperbolic
relative equilibria with a regular polygonal shape do not exist. In particular
the Lagrangian (three equal distances) hyperbolic relative equilibria do not
exist. We also show the existence of a new class of hyperbolic collinear
relative equilibria for the five body problem on surfaces of constant negative
curvature.
