The 30-share Sensex was trading higher by 190.36 points, or 0.57 per cent, at 33,139.57, with all sectoral indices in the green, led by consumer durables, bank, metal and auto.
The gauge had rallied 352.03 points yesterday.
Brokers said unabated buying by retail and domestic institutional investors and a firm trend in other Asian markets influenced sentiment here.
Prominent gainers included Tata Motors, Bharti Airtel, Adani Ports, ICICI Bank, Axis Bank, Maruti Suzuki, ONGC, HDFC Bank, HDFC Ltd, Bajaj Auto, Wipro, TCS, Cipla and SBI, gaining up to 1.68 per cent.
The US Dow Jones Industrial Average ended 0.29 per cent higher in yesterday's trade.
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