Irregular in the sense that such marriages were perfectly valid in terms of Scots Law, although they may well have been illegal, especially at earlier dates, based on laws promoted and implemented by the Established Church of Scotland, - at various eras, the boundaries between the "canon" law of the Auld Kirk and the parliamentary Acts weren't always that clear
The most common form of irregular marriage, to use the old Scots Latin form, was "marriage per verba de praesenti ", involving the declaration of the couple to each other that they agreed to marry.
It is most often stated that such a declaration had to be in the presence of witnesses, which some sources have led me previously to doubt.
I'm currently involved as a lecturer and tutor in the Strathclyde University Postgraduate Certificate in Genealogical Studies.
This is quite fascinating for me, not least because it stretches me and my knowledge, not least in the sense that an answer along the lines of "I think.." or "I believe....." won't suffice.
This has led to a considerable amount of further reading on my part !
In this context, that involved the purchase of the basic work for students on a law course at a Scottish university, J M Thomson's "Family Law in Scotland", 1991, reprinted with Appendix 1993; the author being the Regius Professor of Law at Glasgow University.
Not always an easy book to read in terms of the many new "legal" words needed to be added to my vocabulary, never mind the many Latin phrases
In the context of this post Thomson is perfectly clear that a marriage by declaration in Scots Law - a marriage per verba de praesenti, - did not require witnesses.
However, quite obviously, the absence of such witnesses, made any subsequent attempt to prove the existence of the marriage that more difficult
David