Let (Z_t)_t≥0 be an ℝ_n-valued Lévy process. We consider stochastic differential equations of the dX^x _t = Φ(X^t _t^- )dZ_t X^x ₀ = x, x ∈ ℝ^d, where Φ: ℝ^d → ℝ^d×n is Lipschitz continuous. We show that the infinitesimal generator of the solution process (X^x _t)_t≥0 is a pseudo-differential operator whose symbol p : ℝ^d × → ℝ^d → ℂ can be calculated by p(x, ξ) ≔ -lim_t↓0𝔼^x(e^{i(Xσ _t-x})^⊤ ξ - 1/t). For a large class of Feller processes many properties of the sample paths can be derived by analysing the symbol. It turns out that the process (X^x _t)_t≥0 is a Feller process if Φ is bounded and that the symbol is of the form p(x, ξ) = ψ(Φ^⊤(x)ξ), where ψ is the characteristic exponent of the driving Lévy process.