We revisit the problem of thermal convection in a bidispersive porous medium, first addressed by Nield and Kuznetsov (Int. J. Heat Mass Transfer, 49: 3068-3074, 2006). We investigate the possibility of oscillatory convection by using a highly accurate Chebyshev tau numerical method. We also develop a nonlinear energy stability theory for the same problem. This yields a global stability threshold below which instabilities cannot arise. These thresholds together with the linear instability boundaries yield a zone where thermal instability may be found. The results and theory of Nield and Kuznetsov (Int. J. Heat Mass Transfer, 49: 3068-3074, 2006) are thus proven to be a highly important development in the modern theory of designer porous materials, cf. Nield and Bejan (Convection in Porous Media, Springer, New York, 2006), pp. 94-97.