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Abstract
The first search for the lepton number violating decay K⁺→π⁰π⁻μ⁺e⁺ and lepton flavour violating decays K⁺→π⁰π⁺μ⁻e⁺, K+→π⁰π⁺μ⁺e− has been performed using a dataset collected by the NA62 experiment at CERN in 2016–2018. Upper limits of 2.9×10⁻¹⁰, 3.1×10⁻¹⁰ and 5.0×10⁻¹⁰, respectively, are obtained at 90% CL for the branching ratios of the three decays on the assumption of uniform phase-space distributions.