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We construct quasimodes for some non-selfadjoint semiclassical operators atthe boundary of the pseudo-spectrum using propagation of Hagedorn wave-packets.Assuming that the imaginary part of the principal symbol of the operator isnon-negative and vanishes on certain points of the phase-space satisfying asubelliptic finite-type condition, we construct quasimodes that concentrate onthese non-damped points. More generally, we apply this technique to constructquasimodes for non-selfadjoint semiclassical perturbations of the harmonicoscillator that concentrate on non-damped periodic orbits or invariant torisatisfying a weak-geometric-control condition

Construction of quasimodes for non-selfadjoint operators via propagation of Hagedorn wave-packets