How long should I wait after PhD interview in Denmark? I had a PhD interview last week, the professor send me an email:

Thanks for taking the time to participate in the Skype interview.
We are a bit delayed in making decisions, but I to get back to you on Tuesday 3 November.
Have a nice weekend, 

However, I have not got his Email yet.  What happened?  I wrote a email to him after Tuesday, but no reply. I think that I am just a substitute. I gave up hope of this position. But I really like this project. What can I do?
As you already assume, it's likely that they have settled for another candidate. However, the fact that they didn't reply to your request indicates that they're not quite ready to dismiss you. Maybe their preferred candidate has not agreed to the position yet, and they want to keep their options.

The only thing you can do is write them another polite email, expressing your sincere interest and motivation to do the project, stating again why you think you are the best candidate. In case their first choice declines, you might be in for a good start. 

But in any case, I'd wait out Monday morning, assuming that that's the deadline the other candidate might have negotiated for a decision.