An agile earth-observing satellite equipped with multimode cameras capable of transmitting observation data to other satellites is developed to rapidly respond to requests with multiple observation modes. This gives rise to the Multisatellite Multimode Crosslink Scheduling (MMCS) problem, which involves allocating observation requests to agile satellites, selecting appropriate timing and observation modes for the requests, and transmitting the data to the ground station via the satellite communication system. Herein, a mixed integer programming model is introduced to include all complex time and operation constraints. To solve the MMCS problem, a two-stage heuristic method, called Fast insertion Tabu Search with Conflict-avoidance (FTS-C) heuristic, is developed. In the first stage, a conflict-avoidance insertion algorithm is designed to generate a high-quality initial solution by considering the requests transmission and download. Further, the tabu search-based second stage optimizes the initial solution. Finally, an extensive empirical study based on a real-world situation demonstrates that FTS-C can generate a solution with higher quality in less time than other state-of-the-art algorithms and the CPLEX solver.