  We propose an extension of n-ary Nambu-Poisson bracket to superspace R^{n|m}
and construct by means of superdeterminant a family of Nambu-Poisson algebras
of even degree functions, where the parameter of this family is an invertible
transformation of Grassmann coordinates in superspace R^{n|m}. We prove in the
case of the superspaces R^{n|1} and R^{n|2} that our n-ary bracket, defined
with the help of superdeterminant, satisfies the conditions for n-ary
Nambu-Poisson bracket, i.e. it is totally skew-symmetric and it satisfies the
Leibniz rule and the Filippov-Jacobi identity (fundamental identity). We study
the structure of n-ary bracket defined with the help of superdeterminant in the
case of superspace R^{n|2} and show that it is the sum of usual n-ary
Nambu-Poisson bracket and a new n-ary bracket, which we call \chi-bracket,
where \chi is the product of two odd degree smooth functions.
