This paper addresses the issue of recovering multilevel signals in the presence of slow, frequency nonselective fading and additive white Gaussian noise (AWGN). First, we present a novel noncoherent detector which performs approximate maximum likelihood detection in unknown amplitude and phase (ML-UAP). This ML-UAP detector is implemented using the Viterbi algorithm (VA), which we call the suboptimal noncoherent VA for multilevel signals (SNVA-M). Next, we propose a forgetting-factor based SNVA-M (FSNVA-M) which is quite insensitive to gain and phase changes of the signal, and thereby, avoids the need for explicit carrier recovery and AGC procedures. For differentially encoded multilevel signals, we propose three other schemes namely: symbol-by-symbol differential detector for multilevel signals (SSDD-M), VA-based multiple symbol differential detection for multilevel signals (MSDDVA-M) and the VA-based quotient space approach (QSVA). Finally, we present-results from computer simulations, which indicate that the FSNVA-M detector is best suited for AWGN and Rician fading channels, whereas the SSDD-M, MSDDVA-M and the and SVA detectors are best suited for Rayleigh fading channels. An important feature of all the proposed detectors is that they do not assume any knowledge of the fade statistics. Moreover, they easily lend themselves to DSP-based implementations. © 1998 IEEE.