**C**OMPLEX-VALUED (CV) artificial neural networks have attracted considerable attention from both theoretical research and practical application communities . In particular, the communication signal processing community has long been interested in neural network representations for the CV nonlinear systems as well as in inverting the CV nonlinear systems. Complex-Valued B-Spline Neural Networks for Modeling and Inverting Hammerstein Systems It is well-known that most artificial neural networks cannot be automatically extended from the real-valued (RV) domain to the CV domain because the resulting model would in general violate Cauchyâ€“Riemann conditions, and this means that the training algorithms become unusable. A number of analytic functions were introduced for the fully CV multilayer perceptrons Complex-Valued B-Spline Neural Networks for Modeling and Inverting Hammerstein Systems. A fully CV radial basis function network was introduced in for regression and classification applications. Alternatively, the problem can be avoided using two RV artificial neural networks, one processing the real part and the other processing the imaginary part of the CV signal/system. A more challenging problem is the inversion of a CV nonlinear system, which is typically found in communication signal processing applications. Complex-Valued B-Spline Neural Networks for Modeling and Inverting Hammerstein Systems This is a much under-researched area, and a few existing methods, such as the algorithm proposed in, are not very effective in tackling practical CV signal processing problems. The RV signal processing field offers motivations and inspirations for the development of efficient techniques for modeling and inversion of the CV nonlinear systems. A popular approach to nonlinear systems modeling in the RV domain is to use block-oriented nonlinear models, which comprise the linear dynamic models and static or memoryless nonlinear functions . Complex-Valued B-Spline Neural Networks for Modeling and Inverting Hammerstein Systems In particular, the two types of RV block-oriented nonlinear models that have found wide range of applications are the Wiener model, which comprises a linear dynamical model followed by a nonlinear static transformation, and the Hammerstein model , which consists of a nonlinear static transformation followed by a linear dynamical model. Complex-Valued B-Spline Neural Networks for Modeling and Inverting Hammerstein Systems An efficient B-spline neural network approach for modeling CV Wiener systems was derived in . With its best conditioning property, the RV B-spline curve has been used in computer graphics and computer-aided geometric design .