  There is a remarkable type of field of two-planes special to four dimensions
known as an Engel distributions. They are the only stable regular distributions
besides the contact, quasi-contact and line fields. If an arbitrary two-plane
field on a four-manifold is slightly perturbed then it will be Engel at generic
points. On the other hand, if a manifold admits an oriented Engel structure
then the manifold must be parallelizable and consequently the alleged Engel
distribution must have a degeneration loci -- a point set where the Engel
conditions fails. By a theorem of Zhitomirskii this locus is a finite union of
surfaces. We prove that these surfaces represent Chern classes associated to
the distribution.
