If water isn't the problem behind a sagging ceiling, it may be that the wallboard's nails or screws are coming loose from the joists that they've been driven into, or that the wallboard is dropping down over the nails or screws. Brace the ceiling material with a T-brace (as described previously), carefully easing the wallboard back up to touch the joists. (For a plaster ceiling, you just want to take the weight off the plaster with the brace while you call in an expert. Sagging plaster is not a do-it-yourself fix.)
Locate the joists; you should be able to see a line of indentations or nail pops where the original fastenings were driven into the joists. The original fasteners were probably nails, which by now have likely worked loose. If that's the case, remove them after you've driven screws through the wallboard along the joists at 6-inch intervals (if the nails are still snug, however, you can just hammer them back in after you insert the screws). Countersink the screws slightly (without breaking the wallboard paper) with a dimpler attachment for your drill. Cover the screw heads with three layers of joint compound, sanding between coats, to create a smooth surface (see Chapter 13) that you can then finish to match the rest of the ceiling.
You may find that the tape that seals the wallboard joints has loosened as a result of the sagging. If so, remove the tape, and check the nails or screws on either side of the joint. They'll likely need to be replaced with new screws, to which you can add washers to help support the vulnerable edges of the wallboard. You'll then need to seal the joints with tape and joint compound (as you would for replacing wallboard in Chapter 13).