( CNN ) -- Tropical Storm Arlene appeared to be losing steam as it lumbered across Mexico Thursday , but authorities said the possibility of torrential rains and flooding still threatened many parts of the country . Arlene , the first named storm of the 2011 Atlantic hurricane season , was moving west-southwest at about 7 mph , packing sustained winds of 40 mph , the National Hurricane Center said . It was expected to diminish into a tropical depression later Thursday . Forecasters from the center warned of possible flash floods and mudslides . In Tamaulipas , rains began early Thursday , and precautions were being taken in the southern part of the state , which is expected to be among the hardest hit , said Adan Moctezuma , spokesman for the state government . An alert had been issued in the region , telling residents to prepare for evacuations if necessary . Mexican authorities issued a hurricane warning as Arlene advanced , but that warning had been lifted by Thursday afternoon . A tropical storm warning remained in effect from Tampico , Mexico , south to Barra de Nautla , Mexico . The storm is expected to produce 4 to 8 inches of rain in some areas , while isolated amounts of up to 15 inches could fall in mountainous terrain and could cause life-threatening flash floods and mud slides . The Atlantic hurricane season spans June 1 to November 30 . CNN 's Sean Morris , Chad Myers , Mari Ramos , Ed Payne and Sarah Dillingham contributed to this report .
NEW : Arlene slows , but still packs winds of 40 mph . NEW : A hurricane warning has been lifted along Mexico 's eastern coast . National Hurricane Center : Rains could cause life-threatening flash floods and mudslides .