  We introduce a new mechanism---the forget-remember mechanism into the
spreading process. Equipped with such a mechanism an individual is prone to
forget the "message" received and remember the one forgotten, namely switching
his state between active (with message) and inactive (without message). The
probability of state switch is governed by linear or exponential
forget-remember functions of history time which is measured by the time elapsed
since the most recent state change. Our extensive simulations reveal that the
forget-remember mechanism has significant effects on the saturation of message
spreading, and may even lead to a termination of spreading under certain
conditions. This finding may shed some light on how to control the spreading of
epidemics. It is found that percolation-like phase transitions can occur. By
investigating the properties of clusters, formed by connected, active
individuals, we may be able to justify the existence of such phase transitions.
