We report a numerical investigation of surface plasmon (SP) propagation in ordered and disordered linear chains of metal nanospheres. In our simulations, SPs are excited at one end of a chain by a near-field tip. We then find numerically the SP amplitude as a function of propagation distance. Two types of SPs are discovered. The first SP, which we call the ordinary or quasistatic, is mediated by short-range, near-field electromagnetic interaction in the chain. This excitation is strongly affected by Ohmic losses in the metal and by disorder in the chain. These two effects result in spatial decay of the quasistatic SP by means of absorptive and radiative losses, respectively. The second SP is mediated by longer range, far-field interaction of nanospheres. We refer to this SP as the extraordinary or nonquasistatic. The nonquasistatic SP cannot be effectively excited by a near-field probe due to the small integral weight of the associated spectral line. Because of that, at small propagation distances, this SP is dominated by the quasistatic SP. However, the nonquasistatic SP is affected by Ohmic and radiative losses to a much smaller extent than the quasistatic one. Because of that, the nonquasistatic SP becomes dominant sufficiently far from the exciting tip and can propagate with little further losses of energy to remarkable distances. The unique physical properties of the nonquasistatic SP can be utilized in all-optical integrated photonic systems.