  This paper pursues the study carried out by the authors in {\it Stability and
Hopf bifurcation in the Watt governor system} \cite{smb}, focusing on the
codimension one Hopf bifurcations in the centrifugal Watt governor differential
system, as presented in Pontryagin's book {\it Ordinary Differential
Equations}, \cite{pon}. Here are studied the codimension two and three Hopf
bifurcations and the pertinent Lyapunov stability coefficients and bifurcation
diagrams, illustrating the number, types and positions of bifurcating small
amplitude periodic orbits, are determined. As a consequence it is found a
region in the space of parameters where an attracting periodic orbit coexists
with an attracting equilibrium.

Dynamical Systems