The exact calculation of call blocking probabilities for multiservice ATM networks with alternate or adaptive routing for virtual channels (VC) is hardly possible. Therefore the paper presents and investigates the equivalent single path model as an approximation to omit the VC routing algorithm in the calculation. The model can be applied to ATM networks with several direct virtual path connections between each node pair. Further different methods to calculate the multiservice call blocking probabilities are reviewed and compared. A new approximate method is presented for networks, where the trunk reservation fairness mechanism is applied. This method is accurate, fast and may also be used for noninteger capacities and bandwidth requirements, which is important for statistical multiplexing of variable bitrate traffic.