The positive and negative ions in fuel-rich, pre-mixed flames of CH4 +O-2 +Ar (0.4 <= C/O (atomic basis) <= 0.75) burning at 1 atm have been studied mass spectrometrically. The ions in the most oxygen-rich of these non-turbulent flames were found to be similar to those in more fuel-lean flames, previously studied by Goodings et al. In particular, in this flame, ions are produced in only one chemi-ionisation step in the reaction zone, i.e. by CH+O -> CHO++ e(-). Subsequently a pool of positive ions is then formed rapidly, mainly by protons being transferred from CHO+ to intermediates and final products of combustion. Some negative ions were detected in the reaction zone, but none were found in this flame more than 1 mm downstream of the reaction zone, i.e. in the burnt gas. These negatively charged species, like the positive ions, reflect the presence of intermediates in and near the reaction zone. In the burnt gas, the dominant positive ion, H3O+, recombines with free electrons, the principal negatively charged species, in H3O+ + e(-) -> products. The recombination coefficient was measured to be 2.9 +/- 1.5 x 10(-7) ml ion(-1) s(-1) at similar to 2250 K. However, in the richer oxy-methane flames with C/O >= 0.50, another ion-producing step was found to operate from 1 to at least similar to 5 mm downstream of the reaction zone. This new process is deduced to be CH+ C2H2 -> C3H3++e(-), and maybe involves electronically excited CH radicals. Certainly, C3H3+ becomes the major positive ion in the more fuel-rich flames. The richest flame studied, with C/0=0.75, is weakly sooting; in its burnt gas, both positive and negative ions with masses exceeding 170 a.m.u. were formed throughout the first 8 or so mm of the burnt gas. It is likely that the heavy positive ions are produced by proton transfer from a pool of positive ions (with the primary ion being C3H3+) to precursors of soot, including polyaromatic species. Likewise, the pool of massive negative ions reflects these precursors of soot. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.