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We obtain a large class of cosmological solutions in thetoroidally-compactified low energy limits of string theories in $D$ dimensions.We consider solutions where a $p$-dimensional subset of the spatialcoordinates, parameterising a flat space, a sphere, or an hyperboloid,describes the spatial sections of the physically-observed universe. Theequations of motion reduce to Liouville or $SL(N+1,R)$ Toda equations, whichare exactly solvable. We study some of the cases in detail, and find that undersuitable conditions they can describe four-dimensional expanding universes. Wediscuss also how the solutions in $D$ dimensions behave upon oxidation back tothe $D=10$ string theory or $D=11$ M-theory.Comment: Latex, 21 pages, a reference adjuste

Cosmological solutions in string theories