Judging by the background are you trying to grow this in the tropics? I think rosemary would be doomed in a hot humid climate. Yours looks as if it has a fungal infection. Does the container have drain holes? Is the mix fast draining?

I'm not going to be a lot of help here, but since you haven't gotten a definitive answer yet, I'll help with what I can. I live in south florida and grow culinary rosemary with few problems. Your plants look old to me and I've found all my herbs do better if I trim them up periodically or at least at the end of every growing season - which here is late spring. I keep rosemary in the ground or in clay pots as I think it prefers a bit drier climate. Something is definitely wrong there - maybe a disease or a pest. If they were my plants, I'd take them out of that pot, cut them way back and repot in clay with new soil. I would go to a respected nursery and get their best soil because that is really gonna make a difference in how your plants grow.

Hi :) Would also suggest asking a nursery person. However, that looks to be an older rosemary, with that relatively thick trunk--the pot it's in looks way too small. Did you check to see if it's root-bound? Have you amended the soil since first planting it? Good luck!