A handful of model plants have provided insight into silencing of transposable elements (TEs) through RNA-directed DNA methylation (RdDM). Guided by 24 nt long small-interfering RNAs (siRNAs), this epigenetic regulation installs DNA methylation and histone modifications like H3K9me2, which can be subsequently maintained independently of siRNAs. However, the genome of the clonally propagating duckweed Spirodela polyrhiza (Lemnaceae) has low levels of DNA methylation, very low expression of RdDM components, and near absence of 24 nt siRNAs. Moreover, some genes encoding RdDM factors, DNA methylation maintenance, and RNA silencing mechanisms are missing from the genome. Here, we investigated the distribution of TEs and their epigenetic marks in the Spirodela genome. Although abundant degenerated TEs have largely lost DNA methylation and H3K9me2 is low, they remain marked by the heterochromatin-associated H3K9me1 and H3K27me1 modifications. In contrast, we find high levels of DNA methylation and H3K9me2 in the relatively few intact TEs, which are source of 24 nt siRNAs, like RdDM-controlled TEs in other angiosperms. The data suggest that, potentially as adaptation to vegetative propagation, RdDM extent, silencing components, and targets are different from other angiosperms, preferentially focused on potentially intact TEs. It also provides evidence for heterochromatin maintenance independently of DNA methylation in flowering plants. These discoveries highlight the diversity of silencing mechanisms that exist in plants and the importance of using disparate model species to discover these mechanisms.