Do I need round-trip tickets for me and my wife if I teach for a month at Renmin University?

Hi, you both can apply for business F type with invitation letter from the university. Round-trip ticket is not required if you have the invitation letter. If the letter include your wife's name, she also does't need to provide round-trip ticket. But in case the embassy can only issue tourist L to your wife, the round-trip ticket is required then.