Tokyo, Hong Kong and Sydney declined while Shanghai advanced.
Wall Street's benchmark S&P 500 index rose 0.4% on Friday to a record for a seventh day after U.S. employers hired more people in October than expected.
China's October exports rose 27.1% over a year earlier, though that eased off the previous month's 28.1% growth, customs data showed Sunday.
Despite that gain, Chinese anti-virus controls might dampen factory and consumer activity, “still bringing about an uncertain recovery picture,” Yeap Jun Rong of IG said in a report.
The Nikkei 225 in Tokyo fell 0.1% to 29,570.32 while the Shanghai Composite Index shed 0.2% to 3,497.17. The Hang Seng in Hong Kong lost 0.3% to 24,792.27.
The Kospi in Seoul retreated 0.9% to 2,942.42 and Sydney's S&P-ASX 200 lost 0.2% to 7,440.90.
New Zealand and Bangkok retreated while Singapore and Jakarta gained.
On Wall Street, the S&P 500 rose to 4,697.53 after the government reported the U.S. economy added 531,000 jobs last month, better than the consensus forecast of 450,000.
The Dow Jones Industrial Average gained 0.6% to 36,327.95, also hitting a new high. The Nasdaq composite added 0.2% to 15,971.59.
The U.S. government is due to report inflation this week. Investors are watching price rises amid fears stronger inflationary pressures might prompt the Federal Reserve and other central banks to pull back stimulus that is boosting stock prices.
Also this week, China's ruling Communist Party holds a plenary session, or full meeting of its leaders, military leaders and provincial party bosses. It is the sixth plenum during the latest five-year political cycle that runs through next year.
The sixth plenum usually focuses on ideology and party affairs instead of the economy. However, investors also hope for possible updates on policy toward technology and other industries after data security and anti-monopoly crackdowns on Chinese tech giants that began late last year wiped more than $1 trillion off their total stock market values.
In energy markets, benchmark U.S. crude oil rose $1.11 to $82.38 per barrel in electronic trading on the New York Mercantile Exchange. The contract gained $2.46 to $81.27 on Friday. Brent crude, the price basis for international oils, gained $1.09 to $83.83 per barrel in London. The previous session, it added $2.20 to $82.74.
The dollar gained to 113.62 yen from Friday's 113.40 yen. The euro advanced to $1.1559 from $1.1550.