So after all this, the answer is "There is no American term for this. It's a totally foreign concept for our banking system."
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
The effect of those two lines was that the cheque could not be cashed, but only deposited into a bank account. So an American equivalent would be to endorse a cheque that you issued on the back with the words "For deposit only to credit of (the payee)" as Soothing Dave said above.
Except that if you did that it would no longer be a cheque, but a check.
Last edited by probus; 02-Mar-2013 at 15:16.
When I was a child, I remember my dad drawing two short diagonal lines across his cheques and writing "Payee only" between them. I assumed that was to ensure that no-one apart from the payee could pay them into their bank account. I never really understood that, as I assumed that writing a name on the "Payee" line ensured that.
I don't think we have to cross cheques any more, but I could be wrong - it has been about six years since I last wrote a cheque.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.
So, to summarize, it seems that there's no direct American equivalent of a crossed cheque, but there is a recognized process for achieving the same end: mark it 'for deposit only' - I think that's the wording both Barb and SD used.