Two recent searches for heavy neutral leptons (HNLs) performed with proton-proton collision data recorded at 13 TeV by the CMS experiment are presented. A prompt search in the trilepton final state analyses events with exactly three charged leptons originating from the primary proton-proton interaction vertex, targeting HNL masses between 10 GeV and 1.5 TeV. A displaced search in the dilepton final state analyses events with exactly one prompt charged lepton and a second nonprompt charged lepton associated with a jet and a secondary vertex, targeting HNL masses between 1 and 20 GeV. In both searches, machine-learning methods are applied to separate the HNL signal from the standard model background. Exclusion limits are set on the HNL coupling strength as a function of the HNL mass, covering different mass ranges and HNL scenarios. In several cases, the results exceed previous limits.