[1][2] Turesson attracted interest from both Djurgårdens IF and their rivals Hammarby IF, and chose to join the latter after a successful trial where he impressed manager Folke Adamsson.

[3][4] He immediately broke into the squad as a regular, and formed an offensive partnership with players like Karl-Evert Skoglund, Lars Boman and Lars-Ove Johansson, playing all 22 fixtures as Hammarby finished 9th in the table in 1962.

[1] Back in Allsvenskan 1965, Hammarby was unable to produce any sort of challenge and immediately got relegated from the top division, even though Turesson was voted as the best right-winger in the whole league by Sweden's dominating sports magazine Idrottsbladet.

Tired of bouncing up and down the divisions, during a period when Hammarby was considered as a yo-yo club, Turesson sought a move abroad to play professionally.

Although, Turesson played a major part as Club Brugge won the Belgian Cup in 1970, scoring four goals in five games throughout the tournament.

The club was placed last in the Allvenskan table after eight rounds when he arrived in July, but the winger inspired Hammarby to go practically unbeaten through the rest of the campaign, eventually finishing 5th.

During this period, Turesson was widely regarded as Hammarby's most important player, together with younger talents like Jan Sjöström, Kenneth Ohlsson and Ronnie Hellström.

Hammarby's chairman Lennart Nyman had been in negotiations, that ultimately came out unsuccessful, with several other possible recruitments before convincing Turesson to take the position.