Adam Sutcliffe, in his "Judaism in the Anti-Religious Thought of the Clandestine French Early Enlightenment" [Journal of the History of Ideas 64.1 (2003) 97-117] describes one strand of this clandestine philosophizing in the following way:
There is still a great deal that is unknown about the culture of the French philosophical underground. The manner in which clandestine manuscripts were written, circulated, and discussed remains to a considerable extent a subject on which historians can only speculate. Leading authors and collectors have been identified. It is striking that many intellectuals prominent in the official academies of Paris, such as Bernard Fontenelle, Nicolas Fréret, and Jean Baptiste de Mirabaud, also dabbled in clandestine philosophy. However, in doing so they entered into another conceptual world, sharply segregated from their approved public personae....The ways in which these writers understood the relationship between open and clandestine texts and between their public lives and their clandestine philosophizing is clearly a subject of extreme complexity, and it suggests a striking fluidity in intellectual identities. (pp. 103-104)
There is an excellent online selection of some of the better-known texts (mostly in French) at Clandestine E-Texts from the Eighteenth Century.
It's a very cool topic; and when people ask you what you study, you can say, "Oh, I study Clandestine Enlightenment."
(Cross-posted at Houyhnhnm Land.)
UPDATE: Sharon points out this article by Margaret Jacob, on the works associated with the imprint of Philippe Marteau: The Clandestine Universe of the Eighteenth Century.