In this article, a scheme based on the multimode resonator (MMR) concept is proposed and demonstrated for the design and development of leaky-wave antennas (LWAs) to realize stable radiation properties (e.g., stable radiation efficiency and gain). Firstly, two kinds of traditional LWA unit cells possessing typical single-mode resonator and monotonic changing radiation behaviors are theoretically modeled and analyzed. The condition for LWAs featuring stable radiation properties is then derived, based on which the MMR concept is proposed as a solution for radiation stability. For demonstration purposes, two types of MMR-based unit cells and their associated 1-D periodic LWAs are studied and developed for millimeter-wave applications. One type is based on the magnetoelectric dipole, while the other originates from the aperture-coupled patch antenna. To facilitate the implementation, a detailed design procedure for this class of LWAs is provided in a general manner. The proposed two MMR-based periodic LWAs are modeled, fabricated, and measured. The simulated and measured results are in a reasonable agreement and both illustrate the stability of radiation efficiency and gain performances, thereby demonstrating the correctness and effectiveness of the proposed MMR design concept.