In this thesis we study normal forms of some three dimensional singularities. In this direction we introduce a sl?-invariant family of nonlinear vector elds with a non-semisimple triple zero singularity. Indeed we are concerned with characterization and normal form classi cation of these vector elds. We show that the family constitutes a Lie algebra structure and each vector eld from this family is solenoidal, completely integrable and rotational. All such vector elds share a common quadratic invariant. We provide a Poisson structure for the Lie algebra from which the second invariant for each vector eld can be readily derived. We show that each vector eld from this family can be uniquely characterized by two alternative representatio one uses a vector potential while the other uses two functionally independent Clebsch potentials.