  We perform a general analysis of the dynamic structure of two classes of
relativistic lagrangian field theories exhibiting static spherically symmetric
non-topological soliton solutions. The analysis is concerned with (multi-)
scalar fields and generalized gauge fields of compact semi-simple Lie groups.
The lagrangian densities governing the dynamics of the (multi-) scalar fields
are assumed to be general functions of the kinetic terms, whereas the
gauge-invariant lagrangians are general functions of the field invariants.
These functions are constrained by requirements of regularity, positivity of
the energy and vanishing of the vacuum energy, defining what we call
"admissible" models. In the scalar case we establish the general conditions
which determine exhaustively the families of admissible lagrangian models
supporting this kind of finite-energy solutions. We analyze some explicit
examples of these different families, which are defined by the asymptotic and
central behaviour of the fields of the corresponding particle-like solutions.
  From the variational analysis of the energy functional, we show that the
admissibility constraints and the finiteness of the energy of the scalar
solitons are necessary and sufficient conditions for their linear static
stability against small charge-preserving perturbations. Furthermore we perform
a general spectral analysis of the dynamic evolution of the small perturbations
around the statically stable solitons, establishing their dynamic stability.
Next, we consider the case of many-components scalar fields, showing that the
resolution of the particle-like field problem in this case reduces to that of
the one-component case. The study of these scalar models is a necessary step in
the analysis of the gauge fields.
