A method of identifying failures in an aeroengine, the method comprising the following steps: • using sensors (3a-3f) to collect time-series measurements from said aeroengine and its environment; • using the processor means to calculate from said time-series measurements indicators that are specific to elements of said aeroengine; • using the processor means to define from said specific indicators a set of standardized indicators that are representative of the operation of said aeroengine; • using the processor means to construct an anomaly vector representative of a behavior of said engine as a function of said set of standardized indicators; • using the processor means, in the event of an abnormality being revealed by said anomaly vector, to select a subset of reference vectors having directions belonging to a determined neighborhood of the direction of said anomaly vector, said subset of reference vectors being selected from a set of reference vectors associated with failures of said aeroengine and determined using criteria established by experts, that said set of reference vectors being constructed in accordance with caricatural behaviors of the indicators in the event of anomalies determined by experts; and • using the processor means to identify the failures associated with said subset of reference vectors; wherein selecting said subset of reference vectors comprises the following steps: • using the processor means to calculate geodesic distances between the projection of said anomaly vector and the projections of said reference vectors on a sphere in a space of dimension equal to the number of indicators in said set of standardized indicators minus the number of linear relationships between the indicators; • using the processor means to compare said geodesic distances in pairs; • using the processor means to classify the reference vectors in increasing order of their geodesic distances relative to said anomaly vector; and • using the processor means to form said subset of reference vectors from first reference vectors having a classification order less than a determined rank. • using sensors (3a-3f) to collect time-series measurements from said aeroengine and its environment; • using the processor means to calculate from said time-series measurements indicators that are specific to elements of said aeroengine; • using the processor means to define from said specific indicators a set of standardized indicators that are representative of the operation of said aeroengine; • using the processor means to construct an anomaly vector representative of a behavior of said engine as a function of said set of standardized indicators; • using the processor means, in the event of an abnormality being revealed by said anomaly vector, to select a subset of reference vectors having directions belonging to a determined neighborhood of the direction of said anomaly vector, said subset of reference vectors being selected from a set of reference vectors associated with failures of said aeroengine and determined using criteria established by experts, that said set of reference vectors being constructed in accordance with caricatural behaviors of the indicators in the event of anomalies determined by experts; and • using the processor means to identify the failures associated with said subset of reference vectors; • using the processor means to calculate geodesic distances between the projection of said anomaly vector and the projections of said reference vectors on a sphere in a space of dimension equal to the number of indicators in said set of standardized indicators minus the number of linear relationships between the indicators; • using the processor means to compare said geodesic distances in pairs; • using the processor means to classify the reference vectors in increasing order of their geodesic distances relative to said anomaly vector; and • using the processor means to form said subset of reference vectors from first reference vectors having a classification order less than a determined rank.