Estimation of the temporal derivatives of a noisy position signal is a ubiquitous problem in industrial and robotics engineering. Here, we propose a new approach to get velocity and acceleration estimates of cyclical/periodic signals near to steady-state regime, by using adaptive oscillators. Our method combines the advantages of introducing no delay, and filtering out the high-frequency noise. We expect this method to be useful in control applications requiring undelayed but smooth estimates of velocity and acceleration (e. g., velocity control and inverse dynamics) of quasi-periodic tasks (e. g., active vibration compensation, robot locomotion, and lower-limb movement assistance).