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This article introduces the R package evgam. The package provides functions for fitting extreme value distributions. These include the generalized extreme value and generalized Pareto distributions. The former can also be fitted through a point process representation. Package evgam supports quantile regression via the asymmetric Laplace distribution, which can be useful for estimating high thresholds, sometimes used to discriminate between extreme and non-extreme values. The main addition of package evgam is to let extreme value distribution parameters have generalized additive model forms, the smoothness of which can be objectively estimated using Laplace's method. Illustrative examples fitting various distributions with various specifications are given. These include daily precipitation accumulations for part of Colorado, US, used to illustrate spatial models, and daily maximum temperatures for Fort Collins, Colorado, US, used to illustrate temporal models.