Throughout this paper, k denotes a field of characteristic 0 and all tensor products are over k. Further, k[X;n] is the polynomial algebra in n commuting indeterminates X = (x1, x2, · · · , xn) and Λ[Y ;m] is the Grassmann algebra in n anti-commuting indeterminates Y = (y1, y2, · · · , ym). Supersymmetries are symmetries of supervarieties, i.e., objects, functions on which depend on both usual commuting (even) variables and on anticommuting (odd) ones. For numerous applications of supersymmetry and for basics, see [3], [2] and [10]. Supersymmetries widened the notion of group in order to be able to mix Bose and Fermi particles. However, the collection of morphisms of supervarieties (locally, of its superalgebra of functions F ) — supersymmetries — is not the largest possible group of automorphisms of the algebra F , with superstructure ignored. Besides, not every subalgebra or a quotient of a supercommutative superalgebra is supercommutative, whereas they are metaabelian and the notion of superscheme was first given ([7]) in terms of such, not necessarily homogeneous, subalgebras and quotients of supercommutative superalgebras. Recall that a ring M is said to be metaabelian if [a, [b, c]] = 0 for all a, b, c ∈M , where [a, b] = ab− ba. Volichenko showed (see [8]) that every metaabelian algebra can be realized as a nonhomogeneous subalgebra of a universal supercommutative superalgebra, called its supercommutative envelope. The purpose of this note it to construct an appropriate analog of differential operators on metaabelian algebras, more precisely, viewing a metaabelian algebra M as an analog of the algebra of functions, construct the corresponding algebra of vector fields. Lunts and Rosenberg ([9]) constructed algebras of differential operators on (graded) noncommutative algebras. In particular, one can study differential operators on superalgebras. Superderivations of a superalgebra, which are first order differential operators, form a Lie superalgebra. In a work aborted by his death, Volichenko gave a conjectural intrinsic description of nongraded subalgebras of Lie superalgebras. In his memory then, Leites and Serganova ([8]) called such subalgebras Volichenko algebras and (under a technical assumption) listed simple Volichenko algebras (finite dimensional and of vector fields). Like the list of simple