The conditionality (ancillarity) concept is discussed with particular reference to Durbin's proposed reformulation (C') of Birnbaum's formulation (C) and Fisher's original formulations [6, 7]. It is pointed out that (C') is not in general suitable for applications in the usual sense, since it fails to eliminate all ambiguities of choice of the conditional frame of reference in which standard statistical methods may be applied. The alternative formulations of conditionality are discussed in relation to sufficiency, likelihood, and related methodological problems.