My Exchange 2010 is installed on a 2008R2 server When i do a full backup of the partition were the db and logfiles are located. (VSS enabled) the logfiles are not removed from the system. There are no errors on the backuo job.
You stated that there are no errors on the backup job. Is that based on the backup software or the mailbox databases themselves?
Run Get-MailboxDatabase DatabaseName -Status | select LastFullBackup to confirm when Exchange states there has been a complete backup - not when the backup software states there was a complete backup.
What are you using for backup software? If you are using native Windows see if this applies: The default behavior of WSB is to perform a VSS Copy Backup, which will not truncate the logs. To configure a VSS Full Backup you must configure a Custom backup (not Full Server), add the volumes that contain the Exchange data, click Advanced Settings, and select VSS Full Backup on the VSS Settings tab.
You may be experiencing an Exchange 2010 'feature'. By default, Exchange 2010 keeps 100 logs. You can view the log truncation checkpoint by reading the header information of any of the databases. You can configure this checkpoint (not recommended by Microsoft, but it's possible). MS is currently writing a white-paper/blog on the log truncation checkpoint and it should be available soon.
Actually when a backup software, after backing up the log files in Exchange, will give a trigger to Exchange to purge (remove or truncate) the log files. Even after giving this trigger, depending on the Exchange this action may fail. So, its an issue Exchange environment only.