Recently, traditional real-time systems that played a dedicated role in a limited environment have been evolving to interact with dynamically varying environments. In modern real-time systems, characteristics of real-time tasks such as computational demand and resource allocation can vary over time according to different circumstances, which is referred to as mode transition. In this paper, we focus on the problem of timing guarantees of a set of multi-mode tasks associated with mode transitions and develop an offline schedulability analysis, which does not require any online information; this is an important problem in the real-time systems area. The proposed schedulability analysis not only generalizes an existing framework designed for single-mode tasks, but also significantly improves the state-of-the-art framework designed for multi-mode tasks. Building on the proposed analysis, we also address the problem of enforcing the order of tasks within each mode transition and propose a task-level transition order assignment algorithm, yielding further improvement in schedulability performance. Through simulations, our proposed framework is shown to improve schedulability up to 777.3% over an existing schedulability analysis for multi-mode tasks, depending on the experiment setting under our evaluation environment. INDEX TERMS Real-time scheduling, multi-mode tasks, schedulability analysis, real-time multiprocessor systems.