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In order to construct a massive tensor theory with a smooth massless limit, we apply two kinds of gauge-fixing procedures, that of Nakanishi and that of BRS, to two models of a massive tensor field. The first is of the pure-tensor (PT) type, which describes an ordinary massive tensor field, and the other is of the additional-scalar-ghost (ASG) type, which includes a scalar ghost in addition to the tensor field. It is shown that Nakanishi's procedure can eliminate massless singularities in both models, while the BRS procedure regularizes the ASG model only. The BRS-regularized ASG model is most promising in constructing a complete nonlinear theory.