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The Fleming-Harrington class for right-censored data was first introduced by Harrington and Fleming (1982). This class is widely used in survival analysis studies and it is a subset of the so-called weighted logrank test statistics. Recently, Oller and Gómez (2012) proposed an extension of this class for interval-censored data. This paper introduces the R package FHtest, which implements the Fleming-Harrington class for right-censored and interval-censored survival data. It provides an integrated approach for performing two-sample, k-sample and trend tests based on either counting process theory, likelihood theory, or permutation distributions. In this paper, we summarize the main aspects of the theory framework and present several examples with R codes to illustrate the usage of the main functions of FHtest.