Growing in strength at an alarming rate and pounding Cuba with winds of nearly 150 mph, Hurricane Gustav today continued its threatening march toward the U.S. Gulf Coast today -- with Louisiana right in its path.

The National Hurricane Center said tonight that Gustav is an extremely dangerous Category 4 storm. It could mushroom into the worst category, Category 5, as it heads into the warm waters of the Gulf of Mexico.

"The National Hurricane Center is reporting that the storm went into a high-end Category 3 in 24-hours," Gov. Bobby Jindal said late this afternoon. "On this track, the storm is expected to make landfall Monday on the Louisiana coast, anywhere from New Orleans to Lake Charles, and as a Category 3 or stronger."

Tropical storm winds are forecast to begin around midnight Sunday and a significant storm surge along the Louisiana coast is expected to begin on Monday, Jindal said.

In Louisiana, massive evacuations are under way as a precaution against a repeat of the disaster that was Hurricane Katrina three years ago. Much of the population of Louisiana living south of Interstate 10 has been told to evacuate.

New Orleans Mayor Ray Nagin tonight ordered the mandatory evacuation of that city, turning informal advice to flee from the approaching hurricane into an official order to get out. The evacuation becomes mandatory at 8 a.m. Sunday on the city's vulnerable west bank. It becomes mandatory on the east bank at noon.

Contraflow -- reverse traffic flow in which all lanes on major highways are outbound from the coast -- is to begin all over south Louisiana at 4 a.m. Sunday.

Jindal ordered schools closed in 30 parishes -- including Caddo, Bossier, DeSoto and Webster -- to free up shelter space and bus resources.

Mandatory evacuations were ordered today for Plaquemines, St. Martin, St. Charles, Lafourche, Terrebonne, St. Mary and St. Bernard parishes.

A mandatory evacuation for Calcasieu Parish takes effect at noon Sunday.

Cameron and Iberia parishes can expect mandatory evacuations to be ordered on Sunday, Jindal said.

Buses and trains have begun taking New Orleans' estimated 30,000 residents who are disabled, elderly or don't have transportation to shelters in central and north Louisiana, including Shreveport. They are also being brought to shelters in neighboring states.

The Louisiana National Guard is in New Orleans to assist with evacuations and to prevent looting.

Scientists worry that the storm surge from a major hurricane could reach the top or overtop levees in New Orleans, despite billions spent on rebuilding them after Katrina.

The Associated Press contributed to this report