The multiplicity structure of the hadronic system X produced in deep-inelastic processes at HERA of the type ep → eXY , where Y is a hadronic system with mass M Y < 1.6 GeV and where the squared momentum transfer at the pY vertex, t, is limited to |t| < 1 GeV 2 , is studied as a function of the invariant mass M X of the system X. Results are presented on multiplicity distributions and multiplicity moments, rapidity spectra and forward-backward correlations in the centre-ofmass system of X. The data are compared to results in e + e − annihilation, fixedtarget lepton-nucleon collisions, hadro-produced diffractive final states and to nondiffractive hadron-hadron collisions. The comparison suggests a production mechanism of virtual photon dissociation which involves a mixture of partonic states and a significant gluon content. The data are well described by a model, based on a QCD-Regge analysis of the diffractive structure function, which assumes a large hard gluonic component of the colourless exchange at low Q 2 . A model with soft colour interactions is also successful.