The paper proposes a new method for anomaly detection based on multilinear low-rank models. No a priori knowledge about the investigated system is needed for data-driven parameter identification of these models. Multilinear parameter identification is able to cover more dynamic phenomena than linear black box identification. A minimal model of rank 1 has a tiny number of parameters which is equal to the dynamic order plus the number of inputs. These multilinear parameters are moreover directly interpretable as each parameter indicates the influence of one corresponding state or input to the next state of the MTI model. As example, the method is demonstrated by an anomaly detection with real data from the HVAC system of a test room.