We consider
μ
p
\mu _p
- and
α
p
\alpha _p
-actions on RDP K3 surfaces (K3 surfaces with rational double point (RDP) singularities allowed) in characteristic
p
>
0
p > 0
. We study possible characteristics, quotient surfaces, and quotient singularities. It turns out that these properties of
μ
p
\mu _p
- and
α
p
\alpha _p
-actions are analogous to those of
Z
/
l
Z
\mathbb {Z}/l\mathbb {Z}
-actions (for primes
l
≠
p
l \neq p
) and
Z
/
p
Z
\mathbb {Z}/p\mathbb {Z}
-quotients respectively. We also show that conversely an RDP K3 surface with a certain configuration of singularities admits a
μ
p
\mu _p
- or
α
p
\alpha _p
- or
Z
/
p
Z
\mathbb {Z}/p\mathbb {Z}
-covering by a “K3-like” surface, which is often an RDP K3 surface but not always, as in the case of the canonical coverings of Enriques surfaces in characteristic
2
2
.