Important records could be lost to future generations if local cuts are not reversed, according to the Scottish Council on Archives.
There is a growing interest in tracing family trees
A growing number of tourists have been visiting Scotland to trace their family trees, but some councils do not have enough experts to help them.
The councils have insisted that their archives would still available to the public.
However, genealogists said they were concerned at a reduction in service.
Edinburgh's city archives are closed and the archivists in Argyll and Bute and Dumfries and Galloway were not replaced by full-time staff when they retired.
This comes at a time when some local archives have reported a 50% increase in the number of requests for information.
Professor Irene O'Brien, who chairs the Scottish Council on Archives, said: "The real concern is that we don't have professional staff actually managing the councils' records to make sure they survive for the future.
"What we do today is what helps records survive for the future in 50 or 100 years' time."
She told BBC Scotland that the cutbacks were short-sighted.
"The one-off visitor is obviously affected because they have travelled across the world to use the archives," said Prof O'Brien.
"If they happen to be closed that day, or if the person there does not know the collection well enough and they don't get the service they need, then they come away with a very bad impression of what Scotland's archives are about."