Eager to buy your first home this spring? Already own, but want to trade up? Be warned: there’ll be plenty of competition

Bidding wars have broken out in hot real-estate markets like Denver and Los Angeles, where there aren’t enough houses to meet demand. The lack of supply is a key reason home sales nationwide have yet to return to healthy levels following the housing collapse in 2008.

“Inventory is still fairly low in a lot of markets across the country,” said Skylar Olsen, senior economist at real estate data firm Zillow. “Buyers are not going to have the easiest time out there.”

Further tilting the market in favor of sellers are low mortgage rates, which have ratcheted up pressure on buyers to wrap up deals before borrowing becomes more expensive.

Then there’s the matter of price. While the overall rise in home prices has slowed this year, fierce competition in many cities and markets will make the cost of buying much harder this spring. Prices are peaking or coming close in roughly half the country. Seven states set highs in March, including Colorado, New York, Tennessee and Texas, according to real estate data provider CoreLogic.

There just aren’t enough homes for sale in many parts of the country, and properties are moving fast. In March, one measure showed it would take fewer than five months to sell all the homes on the U.S. market. Normally, it should take six.

Among the toughest markets for buyers: San Jose, San Francisco and Los Angeles, as well as Seattle, Denver, Dallas-Fort Worth, Texas, Nashville and Boston, according to Zillow.