  For a tropical prevariety $V\subset \RR^n$ (being a finite union of rational
polyhedra) two tropical polynomials belong to the same congruence class iff
they coincide on $V$. We define a tropical Hilbert function $TH_V(k)$ as the
dimension of the family of congruence classes of tropical polynomials with
tropical degree at most $k$. It is shown that $TH_V(k)$ coincides with a
polynomial of degree $\dim V$ for sufficiently big $k$ when $V$ is a
polyhedron. For an arbitrary tropical prevariety we formulate it as a
conjecture. The conjecture is justified in case $\dim V =0$.
