Fine webbing and tiny black eggs on rosemary suggest spider mites or a small caterpillar/pest complex. The black specks may be frass (insect droppings) rather than eggs. Accurate identification is essential for effective control.
In the meantime, increase air circulation, avoid overhead watering, and spray with insecticidal soap if mites are suspected.
White Tie-Dye Foliage on Rosemary and Thyme: Need Photo for ID
Cleveland Pear Trunk Damage: Borers or Disease?
Mysterious White Patches on Lemon Tree Bark: Fungus, Canker, or Something Else?
Thick Webbing on Live Oak: Bark Lice (Psocids), Beneficial
White Sticky Globules on Rosemary: Aphids, Mites, or Powdery Mildew?
Diagnosing Browning Leaves on a Japanese Dwarf Red Maple
Identifying and Treating Cochineal Scale on Prickly Pear Cactus
Oak Bark Lice: Beneficial Cleanup Crews
Rooting a Rosemary Cutting in Zone 7b (North Carolina)
Pygmy Palm Fungus Treatment and Patience
Center Impatiens Yellowing in Flower Box? Poor Air Circulation
White Foam on Peppers? Identify and Treat Powdery Mildew Fast
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