In this paper we consider a class of systems of two coupled real scala
r fields in bidimensional spacetime, the main motivation being the stu
dy of the classical or linear stability of soliton solutions. First, w
e present the class of systems and comment on the topological profile
of soliton solutions one can find from the first-order equations that
solve the equations of motion. We then follow the standard approach to
classical stability to introduce the main steps one needs to obtain t
he spectra of Schrodinger operators that appear in this class of syste
ms. We consider a specific system, from which we illustrate the genera
l calculations and present some analytical results. We also consider a
nother, more general, system and present an investigation that introdu
ces new results and offers a comparison with former investigations.