In this paper, we introduce the concepts of -2-absorbing primary subsemimodules
over commutative semirings. Let R be a commutative semiring with identity
and M be an R-semimodule. Let  : S(M) 􀀀! S(M) [ f;g be a function, where S(M)
is the set of subsemimodules of M. A proper subsemimodule N of M is said to be a
-2-absorbing primary subsemimodule of M if rsx 2 N n(N) implies rx 2 N or sx 2 N
or rs 2
p
(N : M), where r; s 2 R and x 2 M. We prove some basic properties of these
subsemimodules, give a characterization of -2-absorbing primary subsemimodules, and
investigate -2-absorbing primary subsemimodules of quotient semimodules.