When does chmod fail?

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http://unix.stackexchange.com – Under what circumstances will chmod fail? I looked at the man page but it only specifies usage and doesn't go into details about what circumstances it won't work in. I'd assume chmod will work if: you're root you own the target file (and are setting a mundane mode bit i.e. not sticky bit, others) Can users use chmod to change permissions on a file they have group access for? Is it related to read/write access? (HowTos)