A subgroup \(H\) of a group \(G\) is called permutable, if \(HK=KH\) for every subgroup \(K\) of \(G\), and \(H\) is S-permutable (Sylow permutable), if \(HS=SH\) for every Sylow subgroup \(S\) of \(G\). A group \(G\) is said to be a PST-group if \(H\) is \(S\)-permutable in \(G\) whenever \(H\) is \(S\)-permutable in \(K\) and \(K\) is \(S\)-permutable in \(G\). Similarly a PT-group is a group in which permutability is transitive. The structures of finite soluble PST-groups and PT-groups were determined by Agrawal and Zacher. Extending this, the present paper describes the structure of locally finite groups in whose finite subgroups Sylow permutability is a transitive relation.