  We present a careful analysis of the temperature dependence of the nuclear
spin-lattice relaxation rate $1/T_1$ in gapped quasi-1D Heisenberg
antiferromagnets. It is found that in order to estimate the value of the gap
correctly from $1/T_1$ the peculiar features of the dispersion curve for the
triplet excitations must be taken into account. The temperature dependence of
$1/T_1$ due to two-magnon processes, is reported for different values of the
ratio $r=J_{\perp}/J_{\parallel}$ between the superexchange constants in a
2-leg-ladder. As an illustrative example we compare our results to the
experimental findings for $^{63}Cu 1/T_1$ in the dimerized chains and
2-leg-ladders contained in Sr$_{14}Cu_{24}O_{41}$
