  For finite-dimensional bifurcation problems, it is well-known that it is
possible to compute normal forms which possess nice symmetry properties.
Oftentimes, these symmetries may allow for a partial decoupling of the normal
form into a so-called ``radial'' part and an ``angular'' part. Analysis of the
radial part usually gives an enormous amount of valuable information about the
bifurcation and its unfoldings. In this paper, we are interested in the case
where such bifurcations occur in retarded functional differential equations,
and we revisit the realizability and restrictions problem for the class of
radial equations} by nonlinear delay-differential equations. Our analysis
allows us to recover and considerably generalize recent results by Faria and
Magalhaes and by Buono and Belair.
