A cleaning method is provided that includes a step of preparing a cleaning composition containing 57 to 95 wt % of (component a) water, 1 to 40 wt % of (component b) a secondary hydroxy group- and/or tertiary hydroxy group-containing hydroxy compound, (component c) an organic acid, and (component d) a quaternary ammonium compound, the composition having a pH of 5 to 10, and a step of removing plasma etching residue formed above a semiconductor substrate by means of the cleaning composition. There are also provided a process for producing a semiconductor device that includes a step of cleaning plasma etching residue formed above a semiconductor substrate using the cleaning method, and a cleaning composition for removing plasma etching residue formed above a semiconductor substrate that contains 57 to 95 wt % of (component a) water, 1 to 40 wt % of (component b) a secondary hydroxy group- and/or tertiary hydroxy group-containing hydroxy compound, (component c) an organic acid, and (component d) a quaternary ammonium compound, the composition having a pH of 5 to 10.