  We investigate the motion of a test particle in a d-dimensional, spherically
symmetric and static space-time supported by a mass $M$ plus a $\Lambda$-term.
The motion is strongly dependent on the sign of $\Lambda$. In Schwarzschild-de
Sitter (SdS) space-time ($\Lambda > 0$), besides the physical singularity at
$r=0$ there are cases with two horizons and two turning points, one horizon and
one turning point and the complete absence of horizon and turning points. For
Schwarzschild-Anti de Sitter (SAdS) space-time ($\Lambda < 0$) the horizon
coordinate is associated to a unique turning point.
