We propose natural generalizations of the credulous and skeptical acceptance problems in abstract argumentation for incomplete argumentation frameworks [3]. This continues earlier work on a similar generalization of the verification problem. We provide a full analysis of the computational complexity of the generalized problems for all original semantics, showing that, in almost all cases, acceptance problems for incomplete argumentation frameworks are significantly harder than the respective problems for argumentation frameworks without uncertainty. All our hardness results for the classes NP, coNP, Π^p₂, and Σ^p₂ are derived from one generic reduction.