  The problem of the stability of solitons in second-harmonic-generating media
with normal group-velocity dispersion (GVD) in the second-harmonic (SH) field,
which is generic to available chi^(2) materials, is revisited. Using an
iterative numerical scheme to construct stationary soliton solutions, and
direct simulations to test their stability, we identify a full
soliton-stability range in the space of the system's parameters, including the
coefficient of the group-velocity-mismatch (GVM). The soliton stability is
limited by an abrupt onset of growth of tails in the SH component, the relevant
stability region being defined as that in which the energy loss to the tail
generation is negligible under experimentally relevant conditions. We
demonstrate that the stability domain can be readily expanded with the help of
two "management" techniques (spatially periodic compensation of destabilizing
effects) - the dispersion management (DM) and GVM management. In comparison
with their counterparts in optical fibers, DM solitons in the chi^(2) medium
feature very weak intrinsic oscillations.
