  A locally compact group G is called a WS-group if the double orbits of the
weakly almost periodic functions on G are relatively weakly compact. It is
known that Moore-groups are WS-groups. We will show that if a discrete FC-group
is a WS-group then its center is of finite index in G. We will study noncompact
locally compact groups with the property that if the double orbits of bounded
continuous functions on G are relatively weakly compact then they are
relatively norm compact. Examples of such groups include the motion group M(n)
and the special linear group SL(n,R).
