  We perform a systematic analysis of the conditions under which
\textit{generalized} gauge field theories of compact semisimple Lie groups
exhibit electrostatic spherically symmetric non-topological soliton solutions
in three space dimensions. By the term \textit{generalized}, we mean that the
dynamics of the concerned fields is governed by lagrangian densities which are
general functions of the quadratic field invariants, leading to physically
consistent models. The analysis defines exhaustively the class of this kind of
lagrangian models supporting those soliton solutions and leads to methods for
their explicit determination. The necessary and sufficient conditions for the
linear stability of the finite-energy solutions against charge-preserving
perturbations are established, going beyond the usual Derrick-like criteria,
which only provides necessary conditions.
