  We study the weak approximation of the second-order backward SDEs (2BSDEs),
when the continuous driving martingales are approximated by discrete time
martingales. We establish a convergence result for a class of 2BSDEs, using
both robustness properties of BSDEs, as proved in Briand, Delyon and M\'{e}min
[Stochastic Process. Appl. 97 (2002) 229-253], and tightness of solutions to
discrete time BSDEs. In particular, when the approximating martingales are
given by some particular controlled Markov chains, we obtain several concrete
numerical schemes for 2BSDEs, which we illustrate on specific examples.
