  Let $X$ be a separable nonquasireflexive Banach space. Let $Y$ be a Banach
space isomorphic to a subspace of $X^*$. The paper is devoted to the following
questions: 1. Under what conditions does there exist an isomorphic embedding
$T:Y\to X^*$ such that subspace $T(Y)\subset X^*$ is total? 2. If such
embeddings exist, what are the possible orders of $T(Y)$?
  Here we need to recall some definitions. For a subset $M\subset X^*$ we
denote the set of all limits of weak$^*$ convergent sequences in $M$ by
$M_{(1)}$. Inductively, for ordinal number $\alpha$ we let
$$M_{(\alpha)}=\cup_{\beta<\alpha}(M_{(\beta)})_{(1)}.$$
  The least ordinal $\alpha$ for which $M_{(\alpha)}= M_{(\alpha+1)}$ is called
the {\it order} of $M$.
