Diffractive dissociation of quasi-real photons at a photon-proton centre of mass energy of W ≈ 200 GeV is studied with the ZEUS detector at HERA. The process under consideration is γp → XN, where X is the diffractively dissociated photon system of mass MX and N is either a proton or a nucleonic system with mass MN < 2 GeV. The cross section for this process in the interval 3 < MX < 24 GeV relative to the total photoproduction cross section was measured to be σDpartial/σtot = 6.2 ± 0.2(stat) ± 1.4(syst)%. After extrapolating this result to the mass interval of mφ2 < MX2 < 0.05W2 and correcting it for proton dissociation, the fraction of the total cross section attributed to single diffractive photon dissociation, γp → Xp, is found to be σSD/σtot = 13.3 ± 0.5(stat) ± 3.6(syst)%. The mass spectrum of the dissociated photon system in the interval 8 < MX < 24 GeV can be described by the triple pomeron (IP IP IP) diagram with an effective pomeron intercept of αIP(0) = 1.12 ± 0.04(stat) ± 0.08(syst). The cross section for photon dissociation in the range 3 < MX < 8 GeV is significantly higher than that expected from the triple pomeron amplitude describing the region 8 < MX < 24 GeV. Assuming that this discrepancy is due to a pomeron-pomeron-reggeon (IP IP IR) term, its contribution to the diffractive cross section in the interval 3 < MX < 24 GeV is estimated to be fIP IP IR = 26 ± 3(stat) ± 12(syst)%. © Springer-Verlag 1997.