Block-oriented models having only one multiplier and the Volterra kernels that describe them are summarized. The kernel estimation of the discrete Volterra series is dealt with. It is pointed out that while the Volterra kernels can easily be derived from the block-oriented models, the structure and the parameters of the block-oriented models cannot be computed in a trivial way from the estimated Volterra kernels. Both graphical and analytical procedures are recommended for the structural identification. The method is supported by several simulation examples.