  We present the current status of a non-perturbative lattice calculation of
the moments of the pion and kaon distribution amplitudes by the RQCD
collaboration. Our investigation is carried out using $N_f=2+1$ dynamical,
non-perturbatively O(a)-improved Wilson fermions on the CLS ensembles with 5
different lattice spacings and pion masses down to the physical pion mass. A
combined continuum and chiral extrapolation to the physical point is performed
along two independent quark mass trajectories simultaneously. We employ
momentum smearing in order to decrease the contamination by excited states and
increase statistical precision.
