The kinematics of the plasma in 14 planetary nebulae (PNe) is analysed by measuring the expansion velocities (Vexp) of different ions as derived from their collisionally excited lines (CELs) and optical recombination lines (ORLs). Vexp is analysed as a function of the ionization potential of ions, which at a first approximation represents the distance of the ion from the central star. In most cases, the kinematics of ORLs is incompatible with the kinematics of CELs at the same ionization potential, especially if CELs and ORLs are considered for the same ion. In general, Vexp from ORLs is lower than Vexp from CELs, indicating that, if the gas is in ionization equilibrium, ORLs are emitted by a gas located closer to the central star. The velocity field derived from CELs shows a gradient accelerating outwards as predicted from hydrodynamic modelling of PNe ionization structures. The velocity field derived from ORLs is different. In many cases, the velocity gradient is flatter or non-existent and highly and lowly ionized species present nearly the same Vexp. In addition, the full width at half-maximum (FWHM) for ORLs is usually smaller than FWHM(CEL). Our interpretation is that ORLs are mainly emitted by a plasma that coexists with the plasma emitting CELs, but does not fit the ionization structures predicted by models. Such a plasma should have been ejected in a different event from the plasma emitting CELs.