The visitors had the first opportunity of the game when John O’Shea, making his debut for the Black Cats, hit the bar with a header from a Sebastian Larsson corner to give the Swans an early scare.
Sunderland again threatened and this time Michel Vorm needed to be at his best to deny Asamoah Gyan when the Ghanaian was put through by Stephane Sessegnon but the keeper came out and made a good block to deny the striker.
Vorm again came to the Swans' rescue after Steven Caulker’s back pass was intercepted by Gyan but the Dutchman was on hand to slide in and take the ball away from the Ghanaian to save the young defender’s blushes.
Brendan Rodgers’ side then rallied after a good Sunderland start and could have gone ahead but Scott Sinclair’s 25-yard effort hit the crossbar after he had brilliantly cut in from the left and rifled a right-footed shot at goal.
The Swans came close again minutes later when Leon Britton jinked through the Black Cats midfield and found Danny Graham in the box but he was well denied by Wes Brown who blocked his shot before it could trouble Simon Mignolet.
Swansea should have taken the lead in the 40th minute when Sunderland failed to clear their lines properly from a corner, the ball was lifted back into the area by Kemy Agustien but Graham put a free header wide of the post from six yards.
The Black Cats could have taken the lead minutes after the restart following a good counter attack involving Sessegnon and Jack Colback but Gyan couldn’t control the ball when he was put through by the Sunderland left-winger and the chance was spurned.
Swansea began to grow into the half and Graham had another opportunity to find the net when he met Neil Taylor’s deep cross but his header was well saved by Mignolet to keep the score at 0-0.
Taylor and Graham combined again minutes later with the left-back finding space to cross the ball which skipped across the box and fell to Graham who took a touch but his left-footed shot was a tame one and fell invitingly into the hands of Mignolet.
Sunderland were reduced to playing on the counter and this tactic nearly yielded dividends when Gyan raced away down the left and could have squared the ball to sub Connor Wickham, who was free in the area, but took the shot on himself and the effort was saved by Vorm.
Both sides were trying to find a winner to secure their first victories of the season but they were frustrated by resolute defending as the game looked destined for a stalemate.
The Black Cats were frustrated again by Vorm as Wickham was put through by Sessegnon but the keeper was out quickly at the feet of the teenager to stop him getting an effort at goal as the hosts were determined to keep their point.
The hosts pressed the visitors late on with possession around the box but were unable to produce a big of magic to break the deadlock and the match finished goalless.
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