Japan's Nikkei 225 rose 0.35 percent, with gains in automakers, trading houses and financials driving the broader rise in the index. Across the Korean strait, the Kospi traded just below the flat line, falling 0.03 percent.
Japan's Nikkei 225 fell 1.19 percent. The Nikkei share average is trading at its lowest since December last year. The ASX 200 dipped 0.05 percent while the Kospi was marginally higher and trading 0.07 percent higher.
The Kospi was down by 0.52 percent, with China-exposed stocks pressured following heightened tensions in the Korean peninsula. Shares for Lotte Shopping, the retail arm of conglomerate Lotte, fell by 1.59 percent, while shares of LG Electronics plunged 1.97 percent.
Japan's Nikkei 225 rose 0.82 percent, recovering most of its losses of 276 points, or 1.44 percent, seen yesterday.
Japanese benchmark Nikkei 225 dropped more than 1.5 percent and the safe-haven yen strengthened.
Chinese mainland shares were mixed on Monday morning, with the Shanghai composite up 0.13 percent and the Shenzhen composite flat. Hong Kong's Hang Seng added 0.21 percent.
During Asian trade, Brent crude futures were up 0.66 percent to USD 52.15 a barrel, and US crude gained 0.57 percent to USD 49.14.
The Shanghai composite was down 0.7 percent and the Shenzhen composite fell 0.59 percent. Hong Kong's Hang Seng plunged 0.96 percent.
Chinese stocks were resiliently higher, with Shanghai composite up 0.03 percent and Shenzhen composite added 0.3 percent. Hong Kong's Hang Seng index was up 0.46 percent.
A combination of mixed global cues as well as implied volatility on expiry day of derivative contracts could keep a check on the market on Thursday. Trends on SGX Nifty indicate a flat opening with a positive bias.
Japan's Nikkei 225 dropped 1.06 percent, likely weighed by the advancing yen as the dollar/yen pair slipped below the 114 handle.
The Shanghai composite opened down 0.1 percent, while the Shenzhen composite opened 0.3 percent lower.
Japanese benchmark Nikkei 225 dropped 0.91 percent, as the yen strengthened against the dollar. A stronger yen is generally bad news for Japanese companies as it makes exports more expensive and lowers repatriated profits earned overseas.
Global, lcoal cues were weak and Indian indices are likely to open flat. SGX Nifty was down at 7974 at the time of writing.
Japan's Nikkei 225 was near flat, down 0.05 percent, ahead of the Bank of Japan (BOJ) monetary policy decision.
In South Korea, the Kospi recovered from earlier losses to trade up 0.17 percent. Hundreds of thousands people rallied in Seoul at the weekend for the fifth straight week of protests against President Park Geun-hye, who is embroiled in a scandal over influence-peddling.
Asian stocks advanced on Thursday, propelled by strong US earnings and oil prices near a 15-month high, as the third and final US presidential debate before the November 8 election got underway.
MSCI's broadest index of Asia-Pacific shares outside Japan gained 0.6 percent. Japan's Nikkei erased earlier gains to stand little changed as the yen advanced.
Equity benchmarks continued to fall on account of weakness in global peers. Hong Kong's Hang Seng and China's Shanghai extended downtrend, falling 2-3 percent.
ICICI Bank and Tata Motors were the biggest losers, down 3-4 percent followed by HDFC, ITC, Axis Bank, L&T and SBI whereas Infosys bucked the trend.
ASX 200 fell 0.36 percent, with a 2.17 percent drop in the energy sector. In Hong Kong, the Hang Seng index was down 0.32 percent in early trade, while Chinese mainland shares were flat.
US stocks closed higher on Monday as investors cheered an election in Japan and extended a jobs-report rally. The S&P 500 index closed at a new all-time high and also posted a new all-time intraday high of 2,143.
In Japan, the Nikkei 225 was up 0.24 percent, while across the Korean Strait, the Kospi was down 0.39 percent.
The Hang Seng index was down 0.4 percent. Chinese mainland markets traded flat, with the Shanghai composite at 2,879.28 and the Shenzhen composite at 1,890.61.
Chinese mainland shares traded higher, with the benchmark Shanghai composite up 0.81 percent and the Shenzhen composite adding 1.39 percent.