δ-Shock wave type solutions in the multidimensional system of conservation laws ρt +∇ · (ρF (U)) = 0, (ρU)t +∇ · (ρN(U)) = 0, x ∈ R , are studied, where F = (Fj) is a given vector field, N = (Njk) is a given tensor field, Fj , Nkj : R n → R, j, k = 1, . . . , n; ρ(x, t) ∈ R, U(x, t) ∈ R. The well-known particular cases of this system are zero-pressure gas dynamics in a standard form ρt +∇ · (ρU...