This paper examines the problem of magnetic merging in a fully collisionless plasma, i.e., a plasma of noninteracting charged particles, explicitly avoiding the fluid (MHD) approximation. The Alfv¿n self-consistency criterion that relates the plasma density to the electric and magnetic fields is shown to be equivalent, when suitably generalized, to the stress-balance requirement discussed by Rich, Vasyliunas, and Wolf. From this criterion the self-consistent electric field and the magnetic merging speed are obtained as functions of the magnetic field configuration and of the icident plasma parameters. The merging speed for equal antiparallel fields is within a factor of 2 of the result of fluid theory if the incident plasma pressure is initially isotropic. The merging speed is respectively reduced or enhanced when the incident parallel plasma pressure P∥ is greater than or less than the incident transverse pressure P⊥. When P∥--P⊥=B2/&mgr;0 (the marginal fire hose stability condition), merging ceases. For the more general field configuration wherein the opposing magnetic fields B1 and B2 have arbitrary magnitudes and directions the merging electric field is shown to have a maximum value when the fields are antiparallel and to decrease monotonically to zero as the angular separation of the fields decreases to arccos (B1/B2). The expected merging electric field at the day side magnetopause as a function of the strength and direction of the interplanetary magnetic field is presented in a form that can be compared directly with observations. Although a detailed comparison is not feasible, the general results of the analysis are compatible with available observations in the magnetosphere and solar wind.