If it was booked together, as it sounds like it was, They will probably cancel the remaining part of the trip. I had a similar problem last year: TPA-EWR-AMS-Vienna(KLM) and return. Wanted to cancel AMS-Vienna portion (was gonna go to CPH instead) about a week out. Was told they would have to reissue the ticket AT THAT DAYS FARES...something like $3000. It didn't make much sense to me as 1) it's a different airline and 2) I told them to keep the fare for the KLM portion, but I think there's no way to do it except by reticketing, therefore the last minute fares.
Ended up booking a cheap ticket on AustriaAir(?) and spent another couple hours enroute rather than pony-up the extra $2000.
edited for early a.m. spelling
[This message has been edited by Sluggo! (edited Mar 07, 2004).]