I had a problem that mail sent from one gmail account to another got bounced back. It shows in the bounced mail that there was a softfail happened.

“mydomain” does not designate xxx.xxx.xxx.xxx as permitted sender

and xxx.xxx.xxx.xxx belongs to one of the gmail’s mail server.

It seems that the gmail server sent the email was not recognized as a valid sender…

Then I found this page,

http://support.google.com/a/bin/answer.py?hl=en&answer=60764

It needs to add “include:_spf.google.com” in the SPF!