  A group $G$ given by a presentation $G = < \mathcal A \| \mathcal R >$ is
called weakly finitely presented if every finitely generated subgroup of $G$,
generated by (images of) some words in $\mathcal A^{\pm 1}$, is naturally
isomorphic to the subgroup of a group $G_0 = < \mathcal A_0 \| \mathcal R_0>$,
where $\mathcal A_0 \subseteq \mathcal A$, $\mathcal R_0 \subseteq \mathcal R$
are finite, generated by (images of) the same words. In the article, weakly
finitely presented periodic groups which are not locally finite are
constructed.
