The present communication addresses the question of the magnitude of dipolar coupling between the lowest electronic transition moments of the DNA nucleosides and its relevance for Frenkel exciton states in double helices. The transition energies and moments of the nucleosides are determined from absorption spectra recorded for dilute water solutions. Dipolar interactions are computed for some typical nucleoside dimers according to the atomic transition charge distribution model. The properties of the exciton states of two particular double helices, (dA)20.(dT)20 and (dAdT)10.(dAdT)10, are calculated considering three closely-lying molecular electronic transitions (S1 and S2 for adenosine, S1 for thymidine). It is shown that (i) the oscillator strength is distributed over a small number of eigenstates, (ii) important mixing of the three monomer electronic transitions may occur, (iii) all eigenstates are spatially delocalised over the whole length of the double helix and (iv) the extent of exciton states over the two strands depends on the base sequence.