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In this paper, by applying the concept of linear prediction, which is widely used for fading channels, to phase- uncertain communications, we generalize existing linear predictive detection algorithms for transmission over channels with phase noise and frequency offset. This approach leads to the derivation of detection algorithms, which are referred to as phasor linear predictive (pLP), for trellis-based maximum a posteriori (MAP) sequence detection (based on the Viterbi algorithm) and MAP symbol detection: trellis-based (using the forward- backward algorithm) and graph-based (using the sum-product algorithm). The effectiveness of the proposed pLP detection algorithms is evaluated for several communication schemes. The derived algorithms outperform previously appeared finite- memory detection solutions in terms of robustness against fast channel dynamics. Moreover, the proposed detection strategy lends itself to attractive extensions to adaptive schemes.