In the paper a new multiple-access protocol, called ATP-1, is analysed. This protocol employs a self-adaptive scheme that switches between two states, the random-access state and the fixed-access state. The analysis is based on an embedded Markov process obtained by examining the system at the beginning of the epochs, which are defined as the intervals of random access state or fixed access state. The epoch duration depends on the number of the busy users at the beginning of the epochs. Finally, the dynamic behaviour of this new scheme is examined in detail using the Markovian properties of the two, above mentioned, protocols.