Agave tequilana is a species of great economic importance for the Mexican society. Like most agaves, it can be propagated either sexually or asexually. However, plants originating from rhizomes are mainly used for commercial production. The aim of this study was to determine the genetic fidelity of plants that were obtained from the field and propagated from rhizomes and of those propagated by in vitro culture methods (somatic embryogenesis and proliferation of axillary buds). We used an inverse ISTR (sequence-tagged repeat) molecular marker based on retrotransposon sequences to detect variability among related individual plants. Cluster analysis showed that plants could be grouped according to the propagation method employed. Plants propagated by the same in vitro method were found to be distinct from those propagated in the field. Even within each method, plants were not genetically identical. Genomic changes were evidenced not only in plants subjected to somaclonal variation in vitro but were also evident in those propagated through the natural asexual process, despite the fact that they were considered true clones. The differences observed in plants confirm the existence of asexual genetic variability.