Yes, it sounds awkward. It should read: The parties undertake to keep two kinds of information secret.
But here's why:
The Parties undertake to keep secret the information received from each other or from third parties and related to fulfillment of the Agreement, supplementary agreements concluded in the execution of the same and any other information obtained in connection with the Agreement independent of the means of obtaining such information.
Thiese green colored parts explain what kind of information that must be secret. This adjective clause was placed close to the word information to explain what kind of information. .
- For Teachers