  We construct a dynamical system based on the KCG (K\"all\'en, Crafoord, Ghil)
conceptual climate model which includes the ice-albedo and
precipitation-temperature feedbacks. Further, we classify the stability of
various critical points of the system and identify a parameter which change
generates a Hopf bifurcation. This gives rise to a stable limit cycle around a
physically interesting critical point. Moreover, it follows from the general
theory that the periodic orbit exhibits relaxation-oscillations which are a
characteristic feature of the Pleistocene ice-ages. We provide an asymptotic
analysis of their behaviour and derive a formula for the period along with
several estimates. They, in turn, are in a decent agreement with paleoclimatic
data and are independent of any parametrization used. Whence, our simple but
robust model shows that a climate may exhibit internal relaxation-oscillations
without any external forcing and for a wide range of parameters.
