  We investigate the stability of $N$-soliton molecules in dispersion-managed
optical fibers with focus on the recently realized 2- and 3-soliton molecules.
We calculate their binding energy using an averaged nonlinear Schr$\rm{\ddot
o}$dinger equation. A combination of variational and numerical solutions to
this equation shows that it describes well the intensity profiles and relative
separations of the experimental molecules. Extending the calculation to larger
values of $N$, the binding energy per soliton is found to saturate at N
$N\ge7$.
