This paper investigates vibration of a moving flexible robot through modal analysis and by constructing vibration spectra of operational signals. A vector autoregressive model combined with a sliding window technique is used for signal processing in order to take into account system nonstationarity. Modal decomposition is conducted on the state matrix constructed from the appropriate vector autoregressive model parameters. A complete modal decomposition and spectrum construction algorithm able of highlighting the structural modes and harmonic excitations is presented. Through accurate identification from the vector autoregressive model, the method presented is able to discriminate, display and monitor the harmonics and structural modes during the processes investigated. This method is validated first by numerical simulation and then experimentally with a flexible robot performing three processes: moving a manipulator through the workspace, steady rotation of a grinder on the end effector and moving the manipulator combined with rotating the grinder. It is found on the operating robot that participation of the first structural mode is negligible when rotating the grinder but must be taken into account when moving the manipulator. The analysis presented and results obtained provide a sound basis for further investigation of vibroimpact behaviour in a robotic grinding process.