A multidimensional cosmological model with space-lime consisting of n
(n greater than or equal to 2) Einstein spaces M(i) is investigated in
the presence of a cosmological constant Lambda and a homogeneous mini
mally coupled scalar field phi(t) as a matter source. Classical and qu
antum wormhole solutions are obtained for Lambda < 0 and all M(i) bein
g 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 spontaneo
us compactification of the internal dimensions with fine tuning of par
ameters.