We consider a simple model describing a closed bosonic string in a constant magnetic field. Exact conformal invariance demands also the presence of a non-trivial metric and antisymmetric tensor (induced by the magnetic field). The model is invariant under target space duality in a compact Kaluza-Klein direction introduced to couple the magnetic field. Like open string theory in a constant gauge field, or closed string theory on a torus, this model can be straightforwardly quantized and solved

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... th its spectrum of states and partition function explicitly computed. Above some critical value of the magnetic field an infinite number of states become tachyonic, suggesting a presence of phase transition. We also construct heterotic string generalisations of this bosonic model in which the constant magnetic field is embedded either in the Kaluza-Klein or internal gauge group sector.