This paper addresses the problem of estimating the frequencies, amplitudes and phases of then sinusoidal components of a possibly biased multi-sinusoidal signal. The proposed adaptive observer allows the direct adaptation of the frequency estimates with a relatively low dynamic order 3n + 1 (3n for an unbiased signal). The stability analysis proves the global exponential convergence of the estimation error and the robustness to additive norm-bounded measurement perturbations. (C) 2018 Elsevier Ltd. All rights reserved.