Long Island home prices climbed to new highs in both counties for at least the third straight month in August, as the limited supply of homes continued to fuel one of the country’s hottest housing markets.

The median price of a single-family home in Nassau County increased 5.4% to a record $875,000 last month, surpassing the previous month’s record high of $860,000, according to data released Friday by OneKey MLS. Two years ago, the median in Nassau County was $750,000.

In Suffolk, the median home price rose 5% to $714,000 compared with a year ago, setting a new high for the county for the fourth consecutive month. The median was just $625,000 two years ago.

Home prices have defied some agents' expectations, rising steadily month after month despite predictions they might level off, s

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