Exclusives require that the writer have some idea what they're doing.
If an agent requests an exclusive by email, and you've just sent out a whole bunch of queries, don't respond immediately. Give it twenty-four hours before you respond so that you can see whether you're going to get another request immediately. Although we all know writers live by their computers when waiting for acceptances, you do have to sleep sometime. So let time work to your advantage for a bit.
Before you accept the exclusive, find out exactly how long the agent wants the exclusive for. Once it goes beyond two weeks, you have to do a cost/benefit analysis. You should not accept an exclusive beyond four weeks.
Then when you accept the exclusive, you want to set a date certain. Let's say an agent asked me today for a two week exclusive (today being 2/7). When I sent the manuscript, I would say that I'm granting a two week exclusive, through 2/23. Notice how I've given the agent a couple of extra days, and I've got a simple date to mark on the calendar.
So tomorrow (Tuesday), another agent wants it. Choice one is to explain the situation to the second agent, and be upfront. Choice two is to stall a bit. Instead of replying immediately, wait. For example, I'd wait until Friday night at about eleven to respond, asking whether the agent wants it by snail mail or email. With any luck, the agent doesn't work until Monday. Then you could ask, in a few more days, whether the agent wants it as a .rtf or .doc file. With a little effort, you can eat up all your time without trying.
Both choices are used in the world, with probably about the same results. Definitely if I had less than a week before the exclusive ran out, I'd just wait. Although a week might seem like a long time, writing is not the major feature of your life, and other things can and do interfere legitimately.
Managing exclusives is a lot about managing the calendar.
Best of luck,
Jim Clark-Dawe