  Let $G$ be a group hyperbolic relative to a collection of subgroups
$\{H_\lambda ,\lambda \in \Lambda \} $. We say that a subgroup $Q\le G$ is
hyperbolically embedded into $G$, if $G$ is hyperbolic relative to $\{H_\lambda
,\lambda \in \Lambda \} \cup \{Q\} $. In this paper we obtain a
characterization of hyperbolically embedded subgroups. In particular, we show
that if an element $g\in G$ has infinite order and is not conjugate to an
element of $H_\lambda $, $\lambda \in \Lambda $, then the (unique) maximal
elementary subgroup contained $g$ is hyperbolically embedded into $G$. This
allows to prove that if $G$ is boundedly generated, then $G$ is elementary or
$H_\lambda =G$ for some $\lambda \in \Lambda $.
