The purpose of this paper is to investigate some difficulties when alethic modalities are introduced into a deontic system. A few deontic theses containing alethic modalities are examined. A generalized Kantian principle that what is deontically evaluated is possible, i.e.,¡u¡µA
¡u¡ºA
, is formulated. This is called the principle of possibility. Another principle, the principle of non-necessity, which states that only non-necessary acts are deontically judged, i.e.,¡u¡µA
¡u~¡¼A
, is also discussed. From these principles, it follows that only contingent acts are subject to deontic evaluation, i.e.,¡u¡µA
¡u¡ºA&¡º~A
, the principle of contingency. It is pointed out that a difficulty arises which cannot be overcome by merely rejecting a necessary act as a genuine act. This is so when we include an alethic concept beyond its logical sense.