Observational evidence suggests that magnetospheric substorms may be associated with the formation of a pair of neutral points or lines in the geomagnetic plasma sheet, containing an X‐type point (or line) and an O‐type one. While magnetic merging theory has concentrated almost entirely on X‐type neutral configurations (points, lines, or sheets), here the role of O‐type configurations is examined, with special attention to three points: (1) How does the X‐O configuration extend in three dimensions? To this end, an analytical model of the configuration was derived, useful for visualizing the geometry and for numerical treatment of plasma flows in it. (2) What modifications are needed in the MHD conditionE = v × Bnear the O‐type line, where it tends to make v grow without limit? By analyzing equations of motion for charged particles near an O‐type neutral line and their solutions in limiting cases, it was found that at a certain distance from the neutral line the mean particle motion became decoupled from that of magnetic field lines (which obeys the MHD condition). The decoupling distance depended on initial conditions in momentum space, suggesting that the MHD approximation which averages out such conditions may not suffice for describing plasma dynamics near the neutral line. Similar problems arise with merging flows near X‐type neutral lines, and although the treatment there is more difficult and requires more approximations, it appears that the same qualitative conclusions apply there as well. (3) What is the role of O‐type neutral lines in particle acceleration? It was found that after inflowing particles are decoupled from the field line motion, they go over to a mode of runaway acceleration along the neutral line. This process is much more efficient along an O‐type line than along an X‐type line, and it is concluded that if merging occurs at an X‐O pair, two particle populations may be expected: low‐energy particles accelerated adiabatically by earthward convection past the X‐type line, dependent mainly on the total amount of flux which has been merged, and high‐energy particles converted toward the O‐type line and undergoing there runaway acceleration. The second acceleration process depends critically on the rapidity of merging and is therefore expected to vary considerably from event to event. All this agrees with observations, and similar processes may also be important in solar flares, where a ‘Y‐type neutral point’ has been proposed, which actually represents the