  Nevanlinna's second main theorem is a far-reaching generalisation of Picard's
Theorem concerning the value distribution of an arbitrary meromorphic function
f. The theorem takes the form of an inequality containing a ramification term
in which the zeros and poles of the derivative f' appear. In this paper we show
that a similar result holds for special subfields of meromorphic functions
where the derivative is replaced by a more general linear operator, such as
higher-order differential operators and differential-difference operators. We
subsequently derive generalisations of Picard's Theorem and the defect
relations.
