Task allocation for heterogeneous agents in disaster environments under time, space and communication constraints is a challenging issue in both theory and practice. This paper presents a dynamic task allocation approach for such situations. The proposed approach consists of an information collection mechanism, a group task allocation mechanism and a group coordination mechanism. Initially, the information collection mechanism is applied to help agents in communication networks to reduce their communication connections and select one agent in each network as the network leader in a decentralized manner so as to facilitate the collection of information for task allocation under communication constraints. Then, the group task allocation mechanism is employed by each network leader to allocate tasks and agents in its network to groups with suitable space ranges by considering time, space and communication constraints as well as the differing capabilities of agents. During task execution, due to the dynamics of disaster environments, the original allocation (by the group task allocation mechanism) of tasks and agents in groups may be unsuitable. To achieve continuous coordination of the heterogeneous agents among groups under communication constraints, the group coordination mechanism is employed. Experimental results demonstrate that the proposed approach can have better performance than many existing approaches in terms of information collection and dynamic task allocation in disaster environments under time, space and communication constraints.