  The purpose of this note is to compare the properties of the symbolic
pseudo-differential calculus on the Heisenberg and on the Engel groups;
nilpotent Lie groups of 2-step and 3-step, respectively. Here we provide a
preliminary analysis of the structure and of the symbolic calculus with symbols
parametrized by $(\lambda,\mu)$ on the Engel group, while for the case of the
Heisenberg group we recall the analogous results on the $\lambda$-classes of
symbols.
