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We consider $\mu_p$- and $\alpha_p$-actions on RDP K3 surfaces (K3 surfaceswith rational double point singularities allowed) in characteristic $p > 0$. Westudy possible characteristics, quotient surfaces, and quotient singularities.It turns out that these properties of $\mu_p$- and $\alpha_p$-actions areanalogous to those of $\mathbb{Z}/l\mathbb{Z}$-actions (for primes $l \neq p$)and $\mathbb{Z}/p\mathbb{Z}$-quotients respectively. We also show thatconversely an RDP K3 surface with a certain configuration of singularitiesadmits a $\mu_p$- or $\alpha_p$- or $\mathbb{Z}/p\mathbb{Z}$-covering by a"K3-like" surface, which is often an RDP K3 surface but not always, as in thecase of the canonical coverings of Enriques surfaces in characteristic $2$.

$\mu_p$- and $\alpha_p$-actions on K3 surfaces in characteristic $p$