Kwapień’s theorem asserts that every continuous linear operator from $$\ell _{1}$$
ℓ
1
to $$\ell _{p}$$
ℓ
p
is absolutely $$\left( r,1\right) $$
r
,
1
-summing for $$1/r=1-\left| 1/p-1/2\right| .$$
1
/
r
=
1
-
1
/
p
-
1
/
2
.
When $$p=2$$
p
=
2
it recovers the famous Grothendieck’s theorem. In this paper we investigate multilinear variants of these theorems and related issues. Among other results we present a unified version of Kwapień’s and Grothendieck’s results that encompasses the cases of multiple summing and absolutely summing multilinear operators.