We present a new class of simple derivations of arbitrary degree in the ring of polynomials in two variables.Let k be a field of characteristic 0 and let R = k [x, y] be the ring of polynomials over k. A derivation δ in the ring R is defined as a k-linear mapping δ :Every derivation δ of the ring R can be uniquely represented in the formthe ring R is called simple if R does not have δ-invariant ideals other than 0 and R. Derivations of this type play an important role in numerous problems. For example, the ring of twisted polynomials R[t, δ] is simple if and only if δ is a simple derivation [1] (Theorem 8.4). Similarly, a Lie algebra defined on the space R according to the rule [a, b] = aδ(b) − δ(a)b is simple if and only if δ is simple [2]. Also recall that, in the case where the derivationis simple, there exist polynomials G such that the quotient module A 2 /A 2 (δ + G) is a simple nonholonomic A 2 -module, where A 2 is a Weyl algebra or an algebra of differential operators on a plane [3] (Theorem 2.