The present invention relates to process for improving the stability and/or preventing the deactivation of the catalyst in processes of manufacture of acetic acid and/or of methyl acetate according to which processes, in a first step, referred to as the reaction step, at least one methyl formate isomerization reaction is carried out in liquid phase, in the presence of carbon monoxide and of a catalytic system comprising at least one halogenated promoter and at least one iridium-based catalytic compound, and, in a second step, referred to as the flash step, the partial vaporization of the reaction medium originating from the first step is carried out in a separator referred to as the flash separator, characterized in that it consists in maintaining an overall content of formic acid and of methyl formate at least equal to 1% by weight of said liquid fraction, preferably between 1 and 50%, preferably between 1 and 30%, by weight with respect to said liquid fraction, in the non-vaporized liquid fraction originating from said flash separator. The invention also relates to a complete process of manufacture acetic acid and/or of methyl acetate which incorporates this improvement. The invention enables preparing acetic acid and/or methyl acetate with an increased stability of the catalytic system, even in the presence of contents of water which are particularly low, and of particularly low carbon monoxide pressures in the reaction zone, and is applied more particularly to processes of manufacture of acetic acid and/or of methyl acetate in which process the first step further comprises a methanol carbonylation reaction.