The paper deals with the synthesis of the coherent asymptotically optimum detector (AOD) for fluctuating targets embedded in non-Rayleigh clutter. For the proposed detection scheme the asymptotic (large sample size) performance is evaluated. Comparison with the linear detector shows that, in principle, significant improvements are achievable by resorting to the AOD if the sample size is arbitrarily large. Since in radar system design the sample size is dictated by technological limits, the paper also investigates by computer simulation the performance of the AOD under such constraints. It turns out that the promises of the asymptotic theory cannot be achieved using moderately large sample sizes. Finally, a rather simple hybrid detection scheme is proposed, that performs better than both the asymptotically optimum and the linear detectors in actual operational situations.