Preserving memory ordering between offloaded instructions and non-offloaded instructions is disclosed. An offload instruction for an operation to be offloaded is processed and a lock is placed on a memory address associated with the offload instruction. In response to completing a cache operation targeting the memory address, the lock on the memory address is removed. For multithreaded applications, upon determining that a plurality of processor cores have each begun executing a sequence of offload instructions, the execution of non-offload instructions that are younger than any of the offload instructions is restricted. In response to determining that each processor core has completed executing its sequence of offload instructions, the restriction is removed. The remote device may be, for example, a processing-in-memory device or an accelerator coupled to a memory.