  The classical Brauer-Siegel theorem states that if $k$ runs through the
sequence of normal extensions of $\mathbb{Q}$ such that $n_k/\log|D_k|\to 0,$
then $\log h_k R_k/\log \sqrt{|D_k|}\to 1.$ First, in this paper we obtain the
generalization of the Brauer-Siegel and Tsfasman-Vl\u{a}du\c{t} theorems to the
case of almost normal number fields. Second, using the approach of Hajir and
Maire, we construct several new examples concerning the Brauer-Siegel ratio in
asymptotically good towers of number fields. These examples give smaller values
of the Brauer-Siegel ratio than those given by Tsfasman and Vl\u{a}du\c{t}
