Demand for offshore rigs in the U.S. Gulf of Mexico has softened after a natural gas drilling boom in the first half of 2001, but forces that could support a recovery may already be at work, analysts said on Monday. Drilling has slowed down in the waters off the Texas and Louisiana coasts in response to a steep drop in U.S. natural gas prices from record highs of around $10 per thousand cubic feet at the end of last year to levels of around $3 in recent weeks. The number of rigs working in the U.S. Gulf fell to 165 last week from 168 the previous week, bringing the utilization rate for the U.S. Gulf drilling fleet down to 77.8 percent from 90.5 percent in late April, according to Offshore Data Services.