The notion of "necessary accidents" seems contradictory, and indeed, literally it is. In Aristotelian metaphysics a difference is held between (1) intelligible content (nature) of a given Substance and (2) further determination of that nature without altering it. A man could be pale without ceasing to be a man. But when omitting the quality "ability of rational behavior or discourse" a man, as human being, ceases to be a man and will then belong to another species. So this "quality" is, in Aristotelian metaphysics, not an accident in the scheme of Categories, and therefore not a quality. It is an essential part of the Substance's nature. A true quality merely adheres to the Substance. However, I cannot see a difference as to ontology between a "quality" of a given Substance and a part of that Substance's "nature". Both are intelligible contents, and when predicated say something about that nature, either its condition or its true content. So when we use the expression "accident" in the present context, we do not necessarily mean something contingent, but just some disposition in its broadest sense. It may be either contingent or necessary.
So with "necessary accidents" is here, i.e. by us [JB], meant the following : Qualities or dispositions (in the broad sense, and thus as "intelligible contents") that necessarily follow from the intrinsic nature of the given Substance, as this Substance is manifested in all individuals of the same species, the species under consideration. Such a quality may either also be present in other Substances (that is in other species), or may only occur in the species under consideration and absent in all other species. In the latter case such a necessary accident is typical of the species and is called a "proprium". It cannot be removed without destroying the species or turning it into another species. There certainly are more than one such "propria" determining the Substance of the individuals of the same species. So a proprium does not only strictly follow from the nature of the given Substance, but cannot be missed, i.e. cannot be removed.
Other "necessary accidents" also follow upon the nature of the given Substance, but, when removed, do not alter this nature. And there are still more "necessary accidents" that are commonly possessed by different species (and thus are not propria), and some of these necessary accidents cannot be missed without destroying the Substance in all these species, while others can be missed. All these accidents are considered to be "necessary" accidents because they are generated by i n t r i n s i c causes, intrinsic with respect to the nature of the given Substance (and different natures may cause the same necessary accident).
It is easy to find examples of these types of "necessary accident" when we compare two or more organismic species as to their intrinsic nature.
On the other hand, in addition to accidents that are necessary (in the ways explained), there are -- certainly in more complex Substances such as organisms -- many contingent accidents (true accidents). They are generated by extrinsic causes, extrinsic with respect to the nature of the given Substance, generated without destroying or altering that nature. Socrates is tanned by the sun.
This conception of "accidents" differs from that of Aristotle and also from that in medieval scholastic philosophy. Further down we will say more about it.