No watches or warnings were posted for either tropical storm, the National Hurricane Center in Miami said in its 5 a.m. EDT advisory.
Nadine, with maximum sustained winds of 60 mph, was about 680 miles south-southwest of the Azores Islands, moving southwest at 6 mph.
Nadine was expected to slowly strengthen during the next 48 hours, forecasters said.
The storm was expected to turn west Thursday then shift to the northwest by Friday.
Tropical storm force winds extended outward from center up to 140 miles.
In the Pacific, Tropical Storm Miriam, with maximum sustained winds of 45 mph, was about 640 miles west of the southern tip of Baja California, Mexico, moving north-northwest at 6 mph.
Forecasters said Miriam was expected to weaken and become a remnant low within the next few days.
The storm was expected to shift to the west and lose some forward speed.
Tropical storm-force winds extended outward from center up to 115 miles.
Forecasters said swells causing life-threatening surf and rip currents could affect the southern and western coasts of the southern tip of Baja California Thursday before beginning to subside Friday.