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Results are presented on event-by-event fluctuations in transverse momentum of charged particles, produced at forward rapidities in p+p, C+C, Si+Si and Pb+Pb collisions at 158 AGeV. Three different characteristics are discussed: the average transverse momentum of the event, the Phi_pT fluctuation measure and two-particle transverse momentum correlations. In the kinematic region explored, the dynamical fluctuations are found to be small. However, a significant system size dependence of Phi_pT is observed, with the largest value measured in peripheral Pb+Pb interactions. The data are compared with predictions of several models. PACS numbers: 14.20.Jn, 13.75.Cs, 12.39.-x