The U.S. economy may still be struggling in some ways, but you wouldn't know it from looking at luxury-car sales.

Global luxury-car heavyweights Mercedes-Benz and BMW (BAMXF 3.93%), the reigning champ, are locked in a fierce battle to lead the U.S. luxury-car market in 2013. Both reported strong sales here in the first quarter -- and several of their rivals posted big gains of their own.

A small market that generates big bucks
The sales volumes are relatively small. In some months, Ford's (F 0.69%) sales of F-Series pickups alone are greater than the total U.S. sales of these two put together. But thanks to impressive margins, luxury cars are big business here and around the world, and BMW and Mercedes, along with Volkswagen's (VWAGY -1.11%) Audi brand, are the Big Three that seem to dominate it just about everywhere.

BMW posted a 13% gain in U.S. sales in March to 27,078 vehicles, marking BMW's best March in the U.S. ever. That increase was powered in large part by gains for its SUVs -- the X3, X5, and X6 in particular, which were together up 40% over year-ago totals.

That's a strong showing, and the company is optimistic about its chances for further gains in the coming months. BMW's North American chief, Ludwig Willisch, said in a statement that he expects the new entry-level 320i model to "accelerate our momentum in the months ahead."

Meanwhile, arch-rival Mercedes-Benz posted a 6.5% year-over-year sales increase for March, with 24,646 sold -- enough for its own record March and first-quarter totals. Strong points were the 34% gains for the company's C-Class sedans, which compete directly with BMW's 3-Series, and a nice result for the company's M-Class SUV.

Mercedes, which is owned by Germany's Daimler (MBGA.F -1.05%), made much of the fact that it posted record sales without launching any new models in the first quarter. The company's U.S. sales chief, Steve Cannon, noted in a statement that coming launches of redesigned E-Class and S-Class models could lead to Mercedes' "strongest year on record" as 2013 continues to unfold.

Other luxury makers are looking strong
Meanwhile, German rival Audi merely posted its 27th straight month of record sales in the U.S., with a 14% gain over good year-ago totals. Continuing the theme, small sedans and SUVs were strong for Audi as well, with a 20% gain for its A4 and a 39% increase for the Q5 SUV. Those gains were achieved with minimal discounting, Audi officials noted, as VW continues to try to maximize its profits outside its troubled European home base.

Toyota's (NYSE: TM) Lexus brand posted a 16% gain for the month and a 15% gain for the quarter behind strong sales of its ES midsized sedan. And General Motors' (GM 1.20%) Cadillac brand continued its slow resurgence, as its ATS sedan -- a surprisingly strong competitor to BMW's 3-Series -- led the way to a 49% year-over-year gain.

Keep watching the auto market in 2013 to see whether luxury vehicles can maintain their sales strength.