  We discuss the occurrence of Poincar\'e-Andronov-Hopf bifurcations in
parameter dependent ordinary differential equations, with no a priori
assumptions on special coordinates. The first problem is to determine critical
parameter values from which such bifurcations may emanate, a solution for this
problem was given by W.-M. Liu. We add a few observations from a different
perspective. Then we turn to the second problem, viz., to compute the relevant
coefficients which determine the nature of the Hopf bifurcation. As shown by J.
Scheurle and co-authors, this can be reduced to the computation of
Poincar\'e-Dulac normal forms (in arbitrary coordinates) and subsequent
reduction, but feasibility problems quickly arise. In the present paper we
present a streamlined and less computationally involved approach to the
computations. The efficiency and usefulness of the method is illustrated by
examples.
