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 decentralised 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. In order 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.Keywords: Dynamic task allocation; Disaster environments; Time, space and communication constraints a task, it first needs to move to the location of the task [7,6,8]; 3) Communication constraints. In disaster environments, due to the destruction of local communication facilities, the amount of information transferred among agents (i.e., the constraint of communication capacities) and the communication distances of agents (i.e., the constraint of communication ranges) are limited [9, 10]. 4) Dynamics of environments. In disaster environments, agents can enter and leave the environments and tasks can be continuously discovered and finished in the environments [11,12]; 5) Differing capabilities of agents. In disaster environments, each agent has its own capabilities, which determine what kind of tasks it can conduct [7]. 6) Local views of agents. Due to the communication constraints of disaster environments, each agent can only acquire the information about tasks close to its location and the information of agents with which it can directly communicate [13];Various approaches have been proposed to achieve efficient task allocation in disaster environments [14,11,15]. Some approaches deal with task allocation through a central point [7,6,8]. In such approaches, the central controller (i.e., the agent in charge of task allocation) can create an optimal solution for task allocation by considering time and space constraints as well as the differing capabilities of agents ...