Health monitoring is performed on CNES spacecraft using two complementary methods: an utomatic Out-Of-Limits (OOL) checking executed on a set of critical parameters after each new telemetry reception, and a monthly monitoring of statistical features (daily minimum, mean and maximum) of another set of parameters. In this paper we present the limitations of this monitoring system and we introduce an innovative anomaly detection method based on machine-learning algorithms, developed during a collaborative R&D action between CNES and TESA (TElecommunications for Space and Aeronautics). This method has been prototyped and has shown encouraging results regarding its ability to detect actual anomalies that had slipped through the existing monitoring net. An operational-ready software implementing this method, NOSTRADAMUS, has been developed in order to further evaluate the interest of this new type of surveillance, and to consolidate the settings proposed after the R&D action. The lessons learned from the operational assessment of this system for the routine surveillance of CNES spacecraft are also presented in this paper.