LetXandYbe normed linear spaces. A linear operatorT:D(T) ⊂X→Yis called anF-operator if its adjointT′:D(T) ⊂Y′→D(T)' is aφ+-operator, i.e. has closed range and finite dimensional-kernel. Characterisations of anF_-operatorTare obtained in the general case and in the case whenTis closable. Unbounded strictly cosingular operators are defined and shown to belong to the class ofF_ -admissible pertubations wheneverYis complete.