Permissions question

I'm hoping this is a pretty simple question. I have a problem were memebers of a group can't delete or overwrite a file. The box is setup several users all part of the same group. Now default umask is 002. The problem I run into is there are processes that add to, del, and over write files. Now if I start this processes and own the files everything works great, but if someone else starts that processes and I own the files it 's hit and miss. Sometimes is works and sometimes there are permissions errors. Any ideas on what could cause this? and yes the processes does have to be ran by other users and its just not practical to change the file owner everytime some else starts the processes nor is it good to set default permissions to rwxrwxrw.

Thanks

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