There are many dynamics that come into play with step-children. Although each situation is different, there are some common issues that are likely to present themselves.
"He's my kid not yours!"
Some people do not feel the same responsibility or authority with their partner's children as they would their own. And sure, I would feel that I have more say with my biological child than my new partner does. This can go the other way too. "He's your kid, not mine."
"You're not my real father!"
It's also understandable that a kid would not feel that their new parent has any authority over them. They took no part in their conception, they did not raise them from birth, and the only reason that they're here is because of someone else's choice, not their own. In addition, it's common for children to feel like their step-parent is trying to replace their real parent - even if they aren't. And it's just up to chance if you and your step-child happen to naturally like each other's personalities.
Other factors include:
Thet age that the step-parent is first introduced - usually the earlier on the easier the adjustment.
The absence, presence, and role of the biological parent in the child's life also influences the dynamic greatly.
If the change is moving from a worse situation to a better one, that could assist with adjustment, and if the change is moving from a better situation to a worse one, that could inhibit adjustment. This goes for all parties involved.
Legally, step-parents have no authority to make decisions about school, medical care, religious practices, or other matters regarding the child's upbringing, whereas two biological parents have equal legal decision-making authority. The balance of power in step-children relationships is a deeply personal matter to work out.
Parents must come to a clear consensus with each other about how much or how little authority the step-parent will have in each specific area of the child's upbringing. I actually recommend drawing up a contract. Not for legal reasons, but for clarity, security, and assurance.
Summary
The best situations are when the child views the step-parent as their real parent, and the step-parent views the step- child as their real child. For some people this happens naturally and quickly, but for others it takes time and effort.