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This work describes the R package gcKrig for the analysis of geostatistical count data using Gaussian copulas. The package performs likelihood-based inference and spatial prediction using Gaussian copula models with discrete marginals. Two different classes of methods are implemented to evaluate/approximate the likelihood and the predictive distribution. The package implements the computationally intensive tasks in C++ using an R/C++ interface, and has parallel computing capabilities to predict the response at multiple locations simultaneously. In addition, gcKrig also provides functions to simulate and visualize geostatistical count data, and to compute the correlation function of the counts. It is designed to allow a flexible specification of both the marginals and the spatial correlation function. The principal features of the package are illustrated by three data examples from ecology, agronomy and petrology, and a comparison between gcKrig and two other R packages.