  A multidimensional cosmological model with space-time consisting of $n (n \ge
2)$ Einstein spaces $M_{i}$ is investigated in the presence of a cosmological
constant $\Lambda$ and a homogeneous minimally coupled scalar field
$\varphi(t)$ as a matter source. Classical and quantum wormhole solutions are
obtained for $\Lambda < 0$ and all $M_{i}$ being Ricci-flat. Classical wormhole
solutions are also found for $\Lambda < 0$ and only one of the $M_{i}$ being
Ricci-flat for the case of spontaneous compactification of the internal
dimensions with fine tuning of parameters.
