How do you address two older ladies when writing a letter? Do you say "mesdames"? Is that the plural of madame?

Thanks.

"Mesdames" is used mostly in directly addressing the persons in questions or a public. A bit tongue-in-cheek, here is an example of addressing a Slow Travel convention in France :

"Monsieur Le Président, Mademoiselle Carla Bruni, Chers Voyageurs Lents, Mesdames et Messieurs!"

Or, when directing the older ladies to their seats at the same Slow Travel convention: "Mesdames, voici vos places!"

The older ladies in reference may expect in writing "Mes chères dames", or "Chères dames", or even possibly "Mesdemoiselles" (again, when addressed directly) or "Chères demoiselles".

So it is all a matter of context and relationship. If this doesn't help, you could post the specific sentence(s).

Thanks, Doru. I want to write a thank you note to two older ladies in Paris, mother and daughter, who invited us into their apartment for tea.

Chère Christy,
if I were you, I would address to only one of them in the very beginning and on the envelope, but would refer to both of them inside the letter.
I would start my letter with "Chère Madame" or "Chère Firstname". Inside I would refer to "vous et votre chère maman".
Oh, by the way, the French - at least among my friends - tend to say Maman more and more and mère less and less. As mère became increasingly co-opted into a couple of eyebrow-raising cuss phrases for the suburban young, the "bourge" crowd is increasingly adopting "maman", leaving "mère" for the, uh, other population section.
Just as Ken has astutely noticed a streamlining of vowels, I have noticed this vocab shift.
Below is an explanation which, in my opinion, uses psy language to avoid mentioning the sociological kidnapping of mère, even though it does say "on parle de plus en plus de « maman », là où il y a quelques années encore, on parlait de « mère »".
http://www.rfi.fr/lffr/articles/087/article_1491.asp