I am 17 years old, my parents are divorced and I live with my mother. Do I have to get my father's permission to go on holiday abroad?

Where are you? UK, Canada, US?

Depending on where you are, you may need both parent's permission to get a passport. If your parents have joint legal custody you may need both parent's permission to leave the country.

Thanks all!! I am in South Africa in the North West Province a town called Klerksdorp. If I already have my passport, do I still need my fathers permission?

I couldn't find anything specific on this online. So the easiest thing for you to do is contact whatever agency issues passports and ask them. You may also need to contact the country where you are planning to go as they may also have restrictions.

Does the custody agreement have anything in it, about travel ?