After posting their 39th consecutive month of year-over-year price gains, home prices in 33 states and the District of Columbia are at or within 10 percent of record highs, according to a report issued today by CoreLogic.

Home prices increased 6.3 percent year-over-year in May, and 1.7 percent month-over-month. Relatively low mortgage rates have helped fuel the price gains. In cities like San Francisco, where there is limited supply and high demand, prices are growing at a double-digit clip.

Prices are so high in certain areas that some economists are starting to worry about localized bubbles. The number of homes on the market is increasing slightly. Total housing inventory at the end of may reached 2.29 million houses, 1.8 percent more than this time last year, according to the National Association of Realtors. That’s a 5.1-month supply, giving sellers a slight edge in today’s market. (A six-month supply is considered a healthy market.)

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South Carolina saw the biggest price gains, with homes showing annual appreciation of 10.3 percent. Other states showing big gains were Colorado (9.8 percent) and Washington (8.8 percent), CoreLogic reports.

High prices have also spurred builders to start constructing new single-family homes, sales of which increased 23 percent year-over-year in May.

While most states have seen price gains, five states (Massachusetts, Connecticut, Maryland, Mississippi, and Louisiana) saw local home prices fall in May.

CoreLogic economists expect prices to increase 5.1 percent year-over-year in June and 0.8 percent month to month.