A method is proposed for monitoring a computer network having at least two subscribers connected via a databus comprising at least two lines, said subscribers having in each case one receiving component and/or one transmitting component. The method is characterized by the fact that the functioning of the databus and/or the functioning of the subscriber is monitored with the aid of error detection signals (watch-dog signals, CEI) of at least one subscriber, and emergency operation measures (M1; M2), matched to the respective error case, for setting defined emergency modes of operation (single-wire mode, special emergency mode) are taken. After taking the first emergency operation measure (M1), it is tested whether the computer network is functioning free of errors. If this is the case, the first emergency operation measure is maintained and thus also the emergency mode of operation (single-wire emergency mode) adopted. If further errors should arise in the computer network after the first emergency operation measure has been taken, the first emergency operation measure is cancelled and the second emergency operation measure (M2) is taken. If, from now on, no further errors arise, the emergency operation mode, the special emergency mode, set by this measure is maintained. Only if further errors continue to arise are the affected subscribers or the entire computer network switched off (bus-off).