Orthogonal modulation, for example, frequency-shift keying (FSK) or pulse-position modulation (PPM), is primarily used in relatively-low-rate communication systems that operate in the power-limited regime. Optimal noncoherent detection of orthogonally modulated signals takes the form of sequence detection and has exponential (in the sequence length) complexity when implemented through an exhaustive search among all possible sequences. In this work, for the first time in the literature, we present an algorithm that performs generalized-likelihoodratio-test (GLRT) optimal noncoherent sequence detection of orthogonally modulated signals in flat fading with log-linear (in the sequence length) complexity. Moreover, for Rayleigh fading channels, the proposed algorithm is equivalent to the maximum-likelihood (ML) noncoherent sequence detector. Simulation studies indicate that the optimal noncoherent FSK detector attains coherent-detection performance when the sequence length is on the order of 100, offering a 3-5 dB gain over the typical energy (single-symbol) detector. While the conventional exhaustive-search approach becomes infeasible for such sequence lengths, the proposed implementation requires a log-linear only number of operations, opening new avenues for practical deployments. Finally, we show that our algorithm also solves efficiently the optimal noncoherent sequence detection problem in contemporary radio frequency identification (RFID) systems.