The author presents a theory of resonant multiphoton ionisation by multimode laser light. He investigates N photon resonant N+1 photon ionisation for a high order bound-bound transition with the resonance dominated by the Stark shift. Two aspects of the problem are considered. He studies the bandwidth dependence for the resonant ionisation probability, approximating the multimode laser light by a chaotic field. Secondly, he investigates the effects of finite mode numbers of the multimode laser. Finally, the theory is compared with the recent experimental results of Lompre et al (1981).