In this work, we report what happens when two large language models respond to each other for many turns without any outside input in a multi-agent setup. The setup begins with a short seed sentence. After that, each model reads the other's output and generates a response. This continues for a fixed number of steps. We used Mistral Nemo Base 2407 and Llama 2 13B hf. We observed that most conversations start coherently but later fall into repetition. In many runs, a short phrase appears and repeats across turns. Once repetition begins, both models tend to produce similar output rather than introducing a new direction in the conversation. This leads to a loop where the same or similar text is produced repeatedly. We describe this behavior as a form of convergence. It occurs even though the models are large, trained separately, and not given any prompt instructions. To study this behavior, we apply lexical and embedding-based metrics to measure how far the conversation drifts from the initial seed and how similar the outputs of the two models becomes as the conversation progresses.