  We define ranks and degrees for families of theories, similar to Morley rank
and degree, as well as Cantor-Bendixson rank and degree, and the notion of
totally transcendental family of theories. Bounds for $e$-spectra with respect
to ranks and degrees are found. It is shown that the ranks and the degrees are
preserved under $E$-closures and values for the ranks and the degrees are
characterized. Criteria for totally transcendental families in terms of
cardinality of $E$-closure and of the $e$-spectrum value, for a countable
language, are proved.
