A measurement is made of the cross section for the process ep → eXY in deep-inelastic scattering with the H1 detector at HERA. The cross section is presented in terms of a differential structure function F2D(3)(xP, β, Q2) of the proton over the kinematic range 4.5 <Q2 <75 GeV2. The dependence of F2D(3) on xP is found to vary with β, demonstrating that a factorisation of F2D(3) with a single diffractive flux independent of β and Q2 is not tenable. An interpretation in which a leading diffractive exchange and a subleading reggeon contribute to F2D(3) reproduces well the xP dependence of F2D(3) with values for the pomeron and subleasing reggeon intercepts of αP(0) = 1.203 ± 0.020(stat.) ± 0.013(sys.)-0.035+0.030(model) and αR(0) = 0.50 ± 0.11(stat.) ± 0.11(sys.)-0.10+0.09(model), respectively. A fit is performed of the data using a QCD motivated model, in which parton distributions are assigned to the leading and subleading exchanges. In this model, the majority of the momentum of the pomeron must be carried by gluons in order for the data to be well described. © Springer-Verlag 1997.