Nonstationary oscillations are ubiquitous in music and speech, ranging from the fast transients in the attack of musical instruments and consonants to amplitude and frequency modulations in expressive variations present in vibrato and prosodic contours. Modeling nonstationary oscillations with sinusoids remains one of the most challenging problems in signal processing because the fit also depends on the nature of the underlying sinusoidal model. For example, frequency modulated sinusoids are more appropriate to model vibrato than fast transitions. In this paper, we propose to model nonstationary oscillations with adaptive sinusoids from the extended adaptive quasi-harmonic model (eaQHM). We generated synthetic nonstationary sinusoids with different amplitude and frequency modulations and compared the modeling performance of adaptive sinusoids estimated with eaQHM, exponentially damped sinusoids estimated with ESPRIT, and log-linear-amplitude quadratic-phase sinusoids estimated with frequency reassignment. The adaptive sinusoids from eaQHM outperformed frequency reassignment for all nonstationary sinusoids tested and presented performance comparable to exponentially damped sinusoids.