Modem communications study

I'm trying to analyze the communications between two old game systems communicating over phone lines via analog modems. The goal is to discover what is inside each packet being sent, in order to design a computer program that can communicate with the game being run on the two older systems. To my knowledge, the technical documentation for these systems has been lost or never been made publicly available. So, basically, I'm looking for a program to "listen in" on the communications between these two systems, and produce some sort of useful logfile, possibly in ASCII or hexidecimal format. The two systems would be connected remotely over the phone lines, and a computer would be connected to the same extension as one of the game systems. I'm not sure if such a program exists, or even exactly what I should be searching for. I'm not even sure if this setup would work. Can anyone give me a hand? Thanks.

Thank you for replying. A friend told me about Wireshark a day or two after I posted this, but I'm glad to have another person confirm it for me. Thank you! :) I'm going to have to set up a very strange connection to get this to work, but Wireshark should be able to get the information I want.