for someone's benefit (usually expressed as `in behalf' rather than `on behalf' and usually with a possessive)
"in your behalf"
"campaigning in his own behalf"
"spoke a good word in his friend's behalf"
as the agent of or on someone's part (usually expressed as "on behalf of" rather than "in behalf of")
"the guardian signed the contract on behalf of the minor child"
"this letter is written on behalf of my client"