about 200 iterations per model around the maximum He luminosity ($\log(L_{\rm He}/L_\odot)\approx 10$).

The helium flash induced mixing found by @FII00 results in a qualitative agreement with the observed surface chemical patterns of stars in the HK survey; however, their theoretical investigation has been performed by using a limited reaction network and a crude procedure to follow the fast mixing process during the HEFM episode. On the other hand the development and the general properties of the HEFM phenomenon strongly depend on where, inside the structure, the ingested hydrogen is burnt. @FII00 assumed that the hydrogen engulfed by the convective zone is mixed instantaneously down to a position at which the lifetime of a proton against capture in the $^{12}\mathrm{C}(p,\gamma)^{13}\mathrm{N}$ reaction is equal to the timescale of convective mixing. We wish to remark that in a previous paper, @HIF90 stated that they adopted a time-dependent mixing scheme which treats convection as a random-walk processes with the rate of convective cell diffusion being a function of the local mixing length and of the local buoyancy velocity. It is not clear to us whether @FII00 still use this approach, or whether they assume instantaneous mixing.

In order to determine how deeply hydrogen 