in a transmission service for connecting a frame relay network to an atm network , a congestion information setting system used in a connection apparatus capable of interfacing between the frame relay network and the atm network , is arranged by : a congestion information extracting unit extracting congestion information from data of one network of either the frame relay network and the atm network ; a mode setting unit combining the extracted congestion information with congestion information of an output side in accordance with a setting condition ; and a congestion information writing unit writing the combined congestion information into data of the other network of either the frame relay network and the atm network in response to a mode set by the mode setting unit . thus the congestion information can be transmitted between different networks .