The flutter monitoring problem is investigated from a detection (and not prediction) point of view, and stated as a statistical hypotheses testing problem regarding a specified damping coefficient. Two flutter onset detection algorithms are described. Both tests build on a residual associated with an output-only subspace-based structural identification method, previously introduced by the authors for structural health monitoring. The first test, working batch wise, handles a null and a close alternative statistical hypotheses on the damping. It comes up from variations on a local asymptotic approximation for the residual, combined with the generalized likelihood ratio (GLR) test. The second test, working on-line, is based on non local hypotheses. It builds on a different approximation for the residual, combined with the cumulative sum (Cusum) test of common use in quality control. Numerical results obtained on real data are discussed, which suggest some interesting properties of the on-line test.