  We introduce a new notion of Almgren's frequency which is adapted to
solutions of a sub-Laplacian (harmonic functions) on a Carnot group of
arbitrary step $\bG$. With this notion we investigate some new functionals
associated with the frequency, and obtain monotonicity formulas for the
relevant harmonic functions, or for the solutions of a closely connected class
of degenerate second order operators of Baouendi type. The results proved in
this paper provide some new insight into the deep link existing between the
growth properties of the frequency, and the local and global structure of the
relevant harmonic functions in these non-elliptic, or subelliptic, settings
