A method for routing connections in a connection-oriented communication network containing switching nodes (Ki) and transmission paths (Uij) between the nodes. Routing processors (RPi) are allocated to said nodes and an alternate route is determined by means of a routing algorithm in a routing system (RSY) according to the frequency of congestion in the transmission paths. ATM connection requests from subscribers are checked in the routing processors (RPi) against the controlled route. A negative decision is indicated when said route is not available for a specific connection request and an overflow message is sent to the routing system (RSY) containing the subscriber's relevant cell rate request and the current fill status of the transmission path. The alternate route is determined by taking into account the frequency of overflow messages for specific cell rate requests from other routes.
