Abstract: The invention makes it possible automatically to detect operation at the limit of stability in an installation for pneumatically conveying a substance in bulk and in dense phase, in which the carrier gas and the bulk substance are injected separately into a lock (3) whose outlet communicates with a duct (4) for pneumatically conveying the bulk substance. The method consists in measuring the "lock" pressure (Pe) which is exerted by the carrier gas in the vicinity of the zone (3a) where the bulk substance is injected into the conveyor duct (4), and in detecting instability in the measured lock pressure (Pe) over a predetermined duration (t), by means of a defined stability criterion. More particularly, the stability criterion consists in performing at least one fuzzy split of the measured pressure values (Pe) in application of a predefined membership function, sampling period, and time interval, and in calculating a stability index on the basis of said fuzzy split.