A function f is called a graceful labelling of a graph G with q edges if f is an injection from the vertices of G to the set (0, 1, 2,..., q) such that, when each edge xy is assigned the label | f(x) — f(y)|, the resulting edge labels are distinct. A graph G is said to be one modulo N graceful (where N is a positive integer) if there is a function  from the vertex set
of G to {0, 1. N, (N + 1), 2N, (2N + 1),..., N(q - 1). N(q -1) + 1} in such a way that (i)  is 1-1 (ii)  induces a bijection * from the edge set of G to {1, N+1, 2N +1,..., N(q - 1)+1} where *(uv) = |(u) - (v)|. In this paper we prove that the acyclic graphs viz. Paths, Caterpillars, Stars and S2,n S2,n are one modulo N graceful for all positive integer N; Lobsters, Banana trees and Rooted tree of height two are one modulo N graceful for N > 1. where Sm,n Sm,n is a graph obtained by identifying one pendant vertex of each Sm,n. This is a fire cracker of subdivisioned stars.