Is it ok for the step parent to punish the children?

I think it's okay to discipline a step child if he/she is in your home...I have a step son and I've talked with his mom and We pretty much have the same views on parenting..I would never spank her son I would feel odd in doing so..But whatever discipline she has set for him or if he is acting out in certain ways that she would like me to address I do so..I have my own rules in my house and he must follow them and he and I have a pretty good relationship...My situations in unique in alot of ways..I am the mother of his big brother and little sister..So with getting back together with my sons dad I accepted his son from his previous marriage as well...We are married now but weren't before we split...