Apache Corp., Chevron, ConocoPhillips and Marathon Oil are among the companies that evacuated workers from installations in the Gulf of Mexico because of Tropical Storm Debby.
"At this time the company has not shut any production on the (continental) shelf due to the disturbance," Apache said in a statement. "Apache is carefully monitoring the situation and if necessary it will order the safe evacuation of all personnel as well as shut in production."
Anadarko Petroleum said some of its production was shut in at some parts of the Gulf of Mexico because of the storm.
The National Weather Service said Monday that the storm was "a little weaker" but was holding its position over the northeastern Gulf of Mexico.
Maximum sustained winds from the storm were reported at 50 miles per hour. There is a 19 percent chance the storm could reach hurricane status by Wednesday.