  The analysis of a birhythmic modified van der Pol type oscillator driven by
periodic excitation and L\`evy noise shows the possible occurrence of coherence
resonance and stochastic resonance. The frequency of the harmonic excitation in
the neighborhood of one of the limit cycles influences the coherence of the
dynamics on the time scale of intrawell oscillations. The autocorrelation
function, the power spectral density and the signal-to-noise-ratio used in this
analysis are shown to be maximized for an appropriate choice of the noise
intensity. A proper adjustment of the L\`evy noise intensity enhances the
output power spectrum of the system, that is, promotes stochastic resonance.
Thus, the robustness of the resonance, that seems to occur also in the presence
of nonstandard noise, is examined using standard measures. The initial
selection of the attractor seems to have an influence on the coherence, while
the skewness parameter of the L\`evy noise has not a notable impact on the
resonant effect.
