This paper studies noise-predictive maximum-likelihood (NPML) detection in the case where noise prediction is accomplished by infinite, rather than finite, impulse-response filters. Two infinite-impulse-response (IIR) NPML detection methods are described. The first one uses an embedding technique to achieve IIR noise prediction in combination with a detector trellis that represents a channel target of the partial-response form. The second one employs a detector trellis that corresponds to a generalized partial-response target, such as the one used for traditional NPML based on finite-impulse-response (FIR) prediction filters, and involves a state-reduction technique to deal with the IIR nature of the overall channel. For both methods, data-dependent (DD) variants of the detection algorithm are developed. Implementation aspects are considered to obtain IIR DD-NPML detectors that are dynamically adaptive on user data. Simulation results are given to illustrate the performance of the different detectors with readback signals captured from an actual tape system at various linear recording densities.