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Let R be a Q-domain,and δ a nonzero locally nilpotent derivation of R.Then,an automorphism expδ of the ring R is defined by (expδ)(a)=∞∑t=0 δl(a)/l! for each a ∈ R.Note that Rδ:= {a ∈R|δ(a)= 0} is a subring of R,and expδ belongs to the automorphism group Aut(R/Rδ)of the Rδ-algebra R.Let LND(R/Rδ)be the set of locally nilpotent Rδ-derivations of R.Then,for each D∈LND(R/Rδ),we have RD(∈)Rδ,and so expD∈Aut(R/RD)(∈)Aut(R/Rδ).Hence,εδ := {expD|D ∈LND(R/Rδ)} is a subset of Aut(R/Rδ).In fact,εδ forms a normal subgroup of Aut(R/Rδ).In this talk,we study the quotient group Aut(R/Rδ)/εδ.For example,let k be a field of characteristic zero,and R = k[x1,x2,x3] the polynomial ring in three variables over k.Then,δ= x2(a)/(a)x1-2x3(a)/(a)x2 is a locally nilpotent derivation of R with Rδ = k[x1x3 + x22,x3].It is well known that the famous automorphism given by Nagata is an element of εδ for this δ.The k-automorphism φ of R defined by φ(x2)=-x2 and φ(xi)= xi for i = 1,3 belongs to Aut(R/Rδ)-εδ.In this case,Aut(R/Rδ)/εδ is a cyclic group of order two generated the image of φ.A special case of Kambayashis Linearization Problem asks whether every finiteorder k-automorphism of the polynomial ring k[x1,…,xn] with(k)= k is linearizable.When R = k[x1,…,xn],the study of Aut(R/Rδ)/εδ is closely related to the study of the Linearization Problem.Actually,every element of Aut(R/Rδ)-εδ has finite order unless R is a polynomial ring in one variable over Rδ.We discuss when εδ equals Aut(R/Rδ)from the view point of linearizability of elements of Aut(R/Rδ)-εδ and triangularizability of δ.We also announce some recent results on the Linearization Problem.