This report presents some initial results from simulations of a linear quasi-anticipatory autonomous agent architecture (ALQAAA), which correspond to a special case of a previously suggested general architecture of anticipatory agents. It integrates low-level reaction with high-level deliberation by embedding an ordinary reactive system based on situation-action rules, called the Reactor, in an anticipatory agent forming a layered hybrid architecture. By treating all agents in the domain (itself included) as reactive agents, this approach drastically reduces the amount of search needed while at the same time requiring only a small amount of heuristic domain knowledge. Instead it relies on a linear anticipation mechanism, carried out by the Anticipator, to achieve complex behaviours. The Anticipator uses a world model (in which the agent is represented only by the Reactor) to make a sequence of one-step predictions. After each step it checks whether the simulated Reactor has reached an undesired state. If this is the case it will modify the actual Reactor in order to avoid this state in the future. Results from both single- and multi-agent simulations indicate that the behaviour of ALQAAA agents is superior to that of the corresponding reactive agents. Some promising results on cooperation and coordination of teams of agents are also presented. In particular, the linear anticipation mechanism is successfully used for conflict detection.