  We present a comprehensive and gauge invariant treatment of perturbations
around cosmological scaling solutions for two canonical scalar fields coupled
through a common potential in the early universe, in the presence of neutrinos,
photons and baryons, but excluding cold dark matter. This setup is relevant for
analyzing cosmic perturbations in scalar field models of dark matter with a
coupling to a quintessence field. We put strong restrictions on the shape of
the common potential and adopt a matrix-eigensystem approach to determine the
dominant perturbations modes in such models. Similar to recent results in
scenarios where standard cold dark matter couples to quintessence, we show that
the stability of the adiabatic perturbation mode can be an issue for this class
of scalar field dark matter models, but only for specific choices of the common
potential. For an exponential coupling potential, a rather common shape arising
naturally in many instances, this problem can be avoided. We explicitly
calculate the dominant perturbation modes in such scenarios.
