In this work we study a class of anharmonic oscillators within the framework of the Weyl-Hörmander calculus.A prototype is an operator on R n of the form (-Δ) + |x| 2k for k, integers ≥ 1.We obtain spectral properties in terms of Schatten-von Neumann classes for their negative powers and derive from them estimates on the rate of growth for the eigenvalues of the anharmonic oscillator (-Δ) + |x| 2k .In particular we give a simple proof for the main term of the spectral asymptotics of these operators.We also study some examples of anharmonic oscillators arising from the analysis on Lie groups.