Sales of previously occupied U.S. homes fell for the second consecutive month in March because there are so few on the market, and the fierce competition for those that do exist are pushing prices to new highs.

Existing home sales fell 3.7% last month from February to a seasonally-adjusted rate of 6.01 million annualized units, the National Association of Realtors said today. Sales jumped 12.3% from March last year.

U.S. median home price surged 17.2% from a year earlier to $329,100, an all-time high. At the end of March, the inventory of unsold homes stood at just 1.97 million. At the current sales pace, that amounts to a 2.1 months’ supply, the NAR said.

“Demand remains strong,” said Lawrence Yun, NAR’s chief economist. “It’s simply a severe lack of supply that is holding back sales.”

Would-be homebuyers across the U.S. are facing perhaps the most competitive market in decades. Any house up for sale typically receives multiple, above-asking-price bids, which pushes prices overall even higher.