Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic properties of the
spectral densities of these random fields are studied. The associated self-similar random fields obtained by applying the Lamperti transformation to GFGCC and GSGCC are studied.
