The harmonic two-colour excitation of a two-level molecule, where the frequencies of the two continuous wave lasers are multiples of a certain frequency, is studied in the rotating wave approximation (RWA) and by using exact methods. Included are the effects of a non-zero different d between the permanent dipole moments of the two states involved in the transition. For two independent frequencies, the two-colour RWA yields analytical results only when one two-colour resonance dominates the transition, while for the harmonic analogue, analytic solutions, exhibiting the effects of both laser and molecular parameters, are available for problems involving competing two-colour resonances. Analytical solutions for both the time-dependent populations of the excited state, and for the associated resonance profiles, are derived, applied to a model two-level molecule, and tested by comparison with exact results obtained using Floquet techniques. The results are used to discuss the phase control of molecular excitation through the interplay of competing resonance involving the effects of d ≠ 0; the competition vanishes if d = 0. Both fixed molecule-laser configurations, and the effects of orientational averaging, are considered.