Existing work on verifying concurrent objects is mostly concerned with safety only, e.g., partial correctness or linearizability. Although there has been recent work verifying lock-freedom of non-blocking objects, much less efforts are focused on deadlock-freedom and starvation-freedom, progress properties of blocking objects. These properties are more challenging to verify than lock-freedom because they allow the progress of one thread to depend on the progress of another, assuming fair scheduling. We propose LiLi, a new rely-guarantee style program logic for verifying linearizability and progress together for concurrent objects under fair scheduling. The rely-guarantee style logic unifies threadmodular reasoning about both starvation-freedom and deadlockfreedom in one framework. It also establishes progress-aware ion for concurrent objects, which can be applied when verifying safety and liveness of client code. We have successfully applied the logic to verify starvation-freedom or d...