Many kinds of proper cores and dominance cores of fuzzy games are proposed in this paper. We also consider two similar concepts of payoff of a fuzzy coalition that are called the true payoff and quasi-payoff. The different concepts of proper cores and dominance cores will be proposed based on the true payoff and quasi-payoff of a fuzzy coalition. Some mild sufficient conditions are provided in this paper to guarantee the equalities of different proper cores and dominance cores.