  Following J.S. Rose, a subgroup H of a group G is said contranormal in G if G
= H^G . In a certain sense, contranormal subgroups are antipodes to subnormal
subgroups. It is well known that a finite group is nilpotent if and only if it
has no proper contranormal subgroups. We prove that a nilpotent-by-finite group
with no proper contranormal subgroup is nilpotent. There are locally nilpotent
groups with a proper contranormal subgroup. We study the structure of
hypercentral groups with a finite proper contranormal subgroup.
