  We present a formalism to extract the dynamical nucleon polarisabilities
defined via a multipole expansion of the structure amplitudes in nucleon
Compton scattering. In contradistinction to the static polarisabilities,
dynamical polarisabilities gauge the response of the internal degrees of
freedom of a composed object to an external, real photon field of arbitrary
energy. Being energy dependent, they therefore contain additional information
about dispersive effects induced by internal relaxation mechanisms, baryonic
resonances and meson production thresholds of the nucleon. We give explicit
formulae to extract the dynamical electric and magnetic dipole as well as
quadrupole polarisabilities from low energy nucleon Compton scattering up to
the one pion production threshold and discuss the connection to the definition
of static nucleon polarisabilities. As a concrete example, we examine the
results of leading order Heavy Baryon Chiral Perturbation Theory for the four
leading spin independent iso-scalar polarisabilities of the nucleon. Finally,
we consider the possible r{\^o}le of energy dependent effects in low energy
extractions of the iso-scalar dipole polarisabilities from Compton scattering
on the deuteron.
