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An independent double Roman dominating function (IDRD-function) on a graph G is a function f :V(G)→ {0, 1, 2, 3} having the property that (i) if f(v) = 0, then the vertex v must have at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3, and if f(v) = 1, then the vertex v must have at least one neighbor w with f(w) 2, and (ii) the subgraph induced by the vertices with positive weight under f is edgeless. The weight of an IDRD-function is the sum of its function values over all vertices, and the independent double Roman domination number (IDRD-number) i_dR(G) is the minimum weight of an IDRD-function on G. The i_dR-stability (i^-_dR-stability, i^+_dR-stability) of G, denoted by st_i_dR (G) (st^-_i_dR (G), st^+_i_dR (G)), is defined as the minimum size of a set of vertices whose removal changes (decreases, increases) the independent double Roman domination number. In this paper, we first determine the exact values on the i_dR-stability of some special classes of graphs, and then present some bounds on st_i_dR (G). In addition, for a tree T with maximum degree Δ, we show that st_i_dR (T)=1 and st^-_i_dR (T)Δ, and characterize the trees that achieve the upper bound. , number=2, journal=European Journal of Pure and Applied Mathematics, year=2025, month=May, pages=5984