The subjet multiplicity has been measured in neutral current e+p interactions at Q2 > 125 GeV2 with the ZEUS detector at HERA using an integrated luminosity of 38.6 pb-1. Jets were identified in the laboratory frame using the longitudinally invariant kT cluster algorithm. The number of jet-like substructures within jets, known as the subjet multiplicity, is defined as the number of clusters resolved in a jet by reapplying the jet algorithm at a smaller resolution scale ycut. Measurements of the mean subjet multiplicity, (nsbj), for jets with transverse energies ET,jet > 15 GeV are presented. Next-to-leading-order perturbative QCD calculations describe the measurements well. The value of αs(MZ), determined from (nsbj) at ycut = 10-2 for jets with 25 < ET,jet < 71 GeV, is αs(MZ) = 0.1187 ± 0.0017(stat.)-0.0009+0.0024(syst.) -0.0076+0.0093(th.). © 2003 Published by Elsevier Science B.V.