We present a clock synchronization algorithm, based on recent results on convergence functions, designed to achieve external and internal synchronization over ATM. We take advantage of transmission delay and delay variation control granted by ATM networks to achieve high precision required to ensure real-time capabilities or distributed data coherence. Precision of the algorithm mainly depends on cell transmission jitter, that introduces uncertainty in time determination. Cell delay variation is heavily reduced by the use of ATM Continuous Bit Rate (CBR) point-to-multipoint connections to exchange timestamps. Besides, the use of the ATM multicast capability grants to reduce the required CBR bandwidth. The algorithm achieves a synchronization closer than 100 microseconds, despite Fclock arbitrary clocks failures and Fcrash node crashes on at least 3Fclock+1+Fcrash nodes. An implementation model for high-precision, combining ATM Operation And Maintainance (OAM) cells and network adapter firmware is described, and is currently implemented in the ANTARA technology.