Methods and apparatuses in a wireless communication system. A method of a first UE comprises: receiving, from a second UE, a first PSCCH and a first PSSCH, wherein the first PSCCH and the first PSSCH include SCI comprising a source ID, a destination ID, and SL DRX time information indicating when the first UE monitors or skips at least one of a second PSCCH and a second PSSCH for the SL DRX operation; configuring SL DRX timers per pair of the source ID and the destination ID; configuring a value of at least one of the SL DRX timers based on information of the SCI; and receiving the at least one of the second PSCCH and the second PSSCH based on the SL DRX timers when the SL DRX operation is applied to a SL communication identified by the pair of the source ID and destination ID.