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Evidence for p-d band crossing at a pressure of 40 kbar is presented for the layered compound TiS2, based on the variation with pressure of the Hall coefficient, RH, thermoelectric power, S, and resistivity, rho . Below 40 kbar the transport properties may be understood within the framework of an extrinsic semiconductor model with strong electron-phonon scattering. Under pressure the band overlap is estimated to change at the rate of 4.5+or-1.5 meV kbar-1; this implies a band gap of 0.18+or-0.06 eV for TiS2 at ambient pressure. Analysis of the quantity -RH/ rho 2e as a function of pressure, and solution of the transport equations at 90 kbar are both used to show that in the semimetallic state of TiS2 the d-band electron mobility exceeds the p-band hole mobility. In contrast, the hole mobility is the greater at all pressures up to 90 kbar in TiSe2.