I can't tell from the photos but jasmine, like most plants, can be affected from a variety of fungus's. You would have to get a more clear picture or do a web search and see if the pictures match what you have.

Good Luck

SCG

Your photo is very dark. Could it be possibly mealy bugs?
They produce honeydew, that could be what you are seeing (sticky substance).
You should get rid of them ASAP, as they spread fast, until you have no choice but discarding the plant. Also can infect any other plants nearby.
If I remember correctly, they like warm & somehow humid environment. Try to mix some rubbing alcohol with water & drop of dish soap and spray everywhere on plant. Or use cotton swab dipped in rubbing alcohol - it takes much longer. You can buy pre-mixed sprays in stores (HD,Lowes and/or garden centres). If spraying, repeat few times. (Spray does not get rid of the eggs, so maybe spray weekly for few weeks?)

There is lots of good advice on other forums (try Cacti&Succulents, or House plants, or Container gardening, probably others) and search by typing subject in search tab (upper right on your screen).
Rina

This post was edited by rina_ on Tue, Nov 19, 13 at 14:33

it looks like scales and scale can bring on fungus too - so this might be a double infection. Remove the scales and the fungus will disappear.