  A system of gluon fields generated at the earliest phase of relativistic
heavy-ion collisions can be described in terms of classical fields. Numerical
simulations show that the system is unstable but a character of the instability
is not well understood. With the intention to systematically study the problem,
we analyze a stability of classical chromomagnetic and chromoelectric fields
which are constant and uniform. We consider the Abelian configurations
discussed in the past where the fields are due to the single-color potentials
linearly depending on coordinates. However, we mostly focus on the nonAbelian
configurations where the fields are generated by the multi-color non-commuting
constant uniform potentials. We derive a complete spectrum of small
fluctuations around the background fields which obey the linearized Yang-Mills
equations. The spectra of Abelian and nonAbelian configurations are similar but
different and they both include unstable modes. We briefly discuss the
relevance of our results for fields which are uniform only in a limited spatial
domain.
