  We define nondegenerate tropical complete intersections imitating the
corresponding definition in complex algebraic geometry. As in the complex
situation, all nonzero intersection multiplicity numbers between tropical
hypersurfaces defining a nondegenerate tropical complete intersection are equal
to 1. The intersection multiplicity numbers we use are sums of mixed volumes of
polytopes which are dual to cells of the tropical hypersurfaces. We show that
the Euler characteristic of a real nondegenerate tropical complete intersection
depends only on the Newton polytopes of the tropical polynomials which define
the intersection. Basically, it is equal to the usual signature of a complex
complete intersection with same Newton polytopes, when this signature is
defined. The proof reduces to the toric hypersurface case, and uses the notion
of $E$-polynomials of complex varieties.
