Let \(f,c_ 1,...,c_{k-2}\) (k\(\geq 3)\) be transcendental meromorphic functions on the complex plane \({\mathcal C}\). Let \(c_ k\in {\mathcal C}- \{0\}\). Let \[ Q=c_ kf^{(k)}+\sum^{k-2}_{m=1}c_ mf^{(m)} \] be not a constant. The paper, generalizing an earlier work, discusses two theorems one of which gives relations between the evB (Borel exceptional values) and the other between the evP (Picard exceptional values) of f and Q under some growth conditions on \(c_ 1,...,c_{k-2}\) in terms of f. E.g. the first theorem asserts that, if (in the usual notation of Nevanlinna theory) \[ T(r,c_ m)=O(T(r,f))\quad as\quad r\to +\infty \text{ for } m=1,...,k-2, \] then either f has no evB or Q has no evB for distinct zeroes except possibly for zero in \({\mathcal C}\). The discussions are extensive and are based on six lemmas. An open problem is posed whether the \(c_ k\) could also be taken as a meromorphic function like the other \(c_ m's\).