It's rather difficult to see the insects in your photo but I'm wondering if they are perhaps soft scale which can sometimes be a pest of
Star Jasmine (Trachelospermum jasminoides) You can use an insecticidal soap ( usually available at Home Depot, Lowes and Wal-Mart garden centers) or you might try mixing a batch of homemade spray if you have the following ingredients on hand:
1 1/2 teaspoons Liquid Dishwashing Soap
1 Quart Water
1 Clean Spray Bottle
Another mixture:
2 Tablespoons Vegetable Oil
2 Tablespoons Liquid Dishwashing Soap
1 Gallon Water
1 Clean Spray Bottle
Mix thoroughly and pour into a spray bottle; thoroughly spray the entire plant, trying to get the stems as well as the backs of the leaves.
*** Note *** Never spray or use any insecticide on plants in direct sunlight ... always do it either in shade or on a cloudy day so that you don't end up with scorched leaves. Also, be sure to LABEL the spray bottle to be certain it is not mistakenly used for something else.
You might find this short article of interest; it was written by one of our members here on All Things Plants:
http://garden.org/ideas/view/S...