[en] We consider perturbations of the semiclassical harmonic oscillator of the form P=-(h²)/2Δ+(x²)/2+h^δW(x), x element of R^m, with W(x)∝ left angle x right angle ^2-μ as vertical stroke x vertical stroke →+∞ and δ,μ element of (0,1), and we investigate the fundamental solution E(t,x,y) of the corresponding time-dependent Schroedinger equation. We prove that at resonant times t=nπ(n element of Z) it admits a semiclassical asymptotics of the form:E(nπ,x,y)∝h^-m(1+ν)/2a₀e^iS(x,y)/h with a₀≠0 and ν=δ/(1-μ), under the conditions x≠(-1)ⁿy and ν<1. (orig.)