too much water
not enough water
(This reminds me of the story of the blind wise men and the elephant: each touches a different part of the elephant and comes to a different conclusion about the whole, none of them being correct.)
After some research of my own, I decided that the most probable cause was a fungal attack and that, other than spraying the plants with all sorts of rubbish, the only course of action was to cut them right back and hope that they will grow again in a rather more healthy state. Another option, of course, would be to remove the plants completely, but that seems a tad drastic just now, so today the old secateurs and pruning saw were retrieved and the plants were cut back to the ground. It's just as well that the weather is cooler today, thanks to a light cloud cover; had I tried to do the job yesterday, I 'd probably have died from heat exhaustion in a very short time.
Now it's wait and see.
Incidentally, oleanders might be very pleasant to look at, at least when they're healthy, but take care with them, as they are highly toxic. It seems that old Napoleon lost several hundred men during his Spanish campaign, simply because they prepared their evening meal using oleander sticks. A few leaves is sufficient to kill a horse, so I've read.
Fortunately, I don't own a horse…