"Nuclear capable" missiles

Occasionally one will see references to the missile programs of various nations referring to a particular missile as “nuclear capable”. What distinct features define such a capacity?

Means that the delivery device (missile) is designed with capability to carry a nuclear payload or a conventional warhead. Keeping in mind when carrying a nuclear payload, the missile must have a minimum range as well as the often touted maximum range. One wouldn’t want to blow oneself up would one?