This dissertation is concerned with the development and performance analysis of non-linear receivers for detection of weak narrow-band signals in multivariate non-Gaussian clutter. The novelty of the detection scheme lies in the utilization of both the complex measurement and the multivariate non-Gaussian character of the clutter. Two clutter models are developed based on the available partial information. Model (I) is based on the a priori knowledge of the first-order density, correlation structure of the amplitude, and the circular symmetric assumption of the in-phase and quadrature phase components. Model (II) is based on the first-order in-phase and quadrature phase densities and the complex correlation structure. These models completely specify a multivariate complex nonGaussian density and can be used for clutter generation. A class of optimum non-linear receiver structures based on weak signal level, canonically known as Locally Optimum Detectors (LOD) are derived under clutter Model (I). This can be considered to be a generalization of the LOD for the independent and identically distributed (i.i.d) clutter. The detectors utilize complex measurements and their structures depend on whether the underlying hypothesis testing model is real or complex. The performance of each of the proposed detector structures, based on the concept of Efficacy, is formulated. Then, the performance of the detectors are evaluated with respect to a reference detector using Asymptotic Relative Efficiency (ARE) criterion. Numerical evaluation of the performance expression is carried out for constant signal in Weibull distribution for various density parameters. Simulation results indicate that the performance of the developed detectors, based on ARE, is superior to (i.i.d) LOD detector and matched filter. Finally, the sensitivity of the detector performance to parameter variation of the structural non-linearities is investigated. / Ph. D.