US inflation figures are expected later in the day and tomorrow the summit between US President Donald Trump and his Chinese counterpart Xi Jinping takes place. By lunchtime many major indices were mixed.
North Sea oil continues its upward trend and is trading at over $105 a barrel on Tuesday morning.
Japan's Nikkei 225 and Topix indexes both rose 0.6 percent.
The Chinese Shenzhen Stock Exchange fell by 0.3 percent while Shanghai was unchanged.
The Hong Kong-based Hang Seng was also up 0.5 percent while the Korean Kospi, which has enjoyed a steady rise in recent days, was down 1.4 percent.
