It sounds like spider mites, a common pest during warm, dry weather. The easiest way of dealing with it is to vigorously hose off the affected plants every day for three days, and then once a week to keep them from coming back until the weather gets moister. This makes it harder for them to hide from their predators under webbing and dust, and makes the environment friendlier to those same predators. The most effective miticides have been taken off the market, and the remaining insecticides that are are effective on mites are even more effective on their predators, compounding the problem. Wettable sulfur dust or spray is effective on mites, but the temps cannot exceed 29º C for 24 hours after application. Soapy water kills mites, but only those that it touches directly. Any hidden survivors repopulate the plant within a few days.