How should I state my peer review experience in the CV? I've been invited to review manuscripts for two journals in my field frequently. I noticed in the first couple of cases my supervisor was the associate editor which has selected me in the process, but for rest of them, I was assigned to the papers by other editors (not from our network).

So, I assumed that my name should be there somewhere in a list, such that the editors may choose me when they see a paper matches my keywords or my previous review results, etc. 

Now, I want to state that in my CV and in a list separate from my ad-hoc review experiences, but I do not know what suitable key phrase I should use.

For instance, can I use the following?


  Member of the review board for Journals X and Y


By the way, I work in the field of computer science.
This is the sort of thing which will vary more from field to field, and you may want to talk to other people in your field, but my general inclination is not to do so. Unless you have been specifically told that there is some review board you are on, or been invited to be on, this may not even exist. Aside from the ethics, if this is a prominent journal, and one of the editors sees your CV, they could react extremely negatively. A better solution might be that if you are going to list what journals you have reviewed for is to list how many articles you have reviewed for a journal if you have reviewed more than one.