Gwenno, thank you! I searched through the dormant threads, but could not discover it. I'm afraid my gardening skills are better than my thread-necromancy skills.
Anent your rosemary: where is it growing? Out in the garden or inside? Rosemary is quite tolerant of both heat and cold (that's why you so often find it in Christmas decorations), but, like its relative lavender, it doesn't like humidity or full shade. My rosemary bushes do best in full sun, even in our horribly hot summers, being subject to moulds and other fungal diseases if it gets too cold, dark and wet.
The other thing rosemary likes is good air circulation, that is, having the air moving around its branches, to prevent the buildup of moisture. It also needs very good drainage; having standing water around the roots is certain to make it rot. Rosemary likes a slightly alkaline soil, so if your soil is acidic give it a sprinkle of lime. If the problem seems to be a mould or fungus, I'd say cut off the affected bits and dispose of them by burning or putting them in the rubbish, water it, including the foliage, with one part milk to four parts water (sounds weird but works), and if it is in a pot, move it to somewhere with lots of air and sun. There are commercial fungicides you can use, but many of those also kill the soil biota.
Which rosemary cultivar do you have? My hardiest ones are 'Blue Lagoon' which has large very dark blue flowers, a white-flowered form, the pink-flowered trailing form and 'Silver Laced' with its white-striped leaves and pale blue flowers, all of which are fairly modern cultivars developed within the last few centuries, and another unnamed one which I grew from a cutting of the rosemary hedge along the driveway at Cave House, taken when I lived there about twenty years ago. Those five grow in shallow sandy/gravelly soil, right out in the open, exposed to frost and blazing sun, and they do fine. The one from Cave House is particularly tough, when I came there it was growing as a long hedge along the drive, exposed to all weathers on a very windy hilltop, and had been completely neglected for at least twenty years. The bushes were gnarly and twisted with weather, planted in gravel against an old stone wall, but only a few had died, and the scent and the flowers were amazing - our summer honey was always wonderful there.
I also have the cultivars 'Benenden Blue', which has very fine leaves and bright blue flowers, and 'Gold Laced' which has a pale blue flower and leaves with a gold stripe. Those two can tolerate part shade, one being on the eastern side of my house so it gets only morning sun, the other is under partial summer shade, growing between the jujube tree and the Early Settler peach, both of which are deciduous so it gets winter sun.