The term comes from the word "conclave", which is used in relation to mainstream Catholic papal elections. Conclavists tend to be strongly opposed by other Traditionalist Catholics, including the sedevacantists with whom they share the belief that the official succession of popes is invalid.
Conclavism as a phenomenon is inextricably linked with sedevacantism, which itself developed in the late 1960s and 1970s, in the years following the Second Vatican Council. It was some time, however, before any individuals or groups progressed from the claim that the Holy See was vacant to the enterprise of electing a new pontiff.
As can be seen from the following section, conclavism in the strict sense seems to have been primarily a phenomenon of the 1990s, and is particularly associated with the English-speaking world.
Technically distinct from the above conclavist antipopes is the cateogry of "popes" whose claims to the papacy derive from alleged divine revelations or apparitions. In these cases, there is no "conclave" process, and hence the term "conclavism" is arguably inappropriate.
The first post-Vatican II antipope, Gregory XVII of the Palmarian Catholic Church, whose papal claim was asserted in 1978, fell into this category. Other antipopes of the same sort include the following:
Alleged divine appointment was also the basis for the pre-Vatican II (1950) claim of Michel Colin to the papacy as Clement XV. Colin's sect survives, divided into different factions, to this day.
The Legio Maria movement of Kenya can be considered as a special case within conclavism. It has its own popes and ecclesiastical structure, having broken with the official Church in the early 1960s, but it is geographically and ethnically concentrated in western Kenya and has no connection with sedevacantism or the doctrinal underpinnings of other conclavist groups. The current Legio Maria pope is Raphael Titus Otieno.