For a graph G, let f:V(G)→P({1,2}).\documentclass[12pt]{minimal}
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\begin{document}$$f:V(G)\rightarrow \mathcal {P}(\{1,2\}).$$\end{document} If for each vertex v∈V(G)\documentclass[12pt]{minimal}
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\begin{document}$$v\in V(G)$$\end{document} such that f(v)=∅\documentclass[12pt]{minimal}
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\begin{document}$$f(v)=\emptyset $$\end{document} we have ⋃u∈N(v)f(u)={1,2},\documentclass[12pt]{minimal}
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\begin{document}$$\bigcup \nolimits _{u\in N(v)}f(u)=\{1,2\},$$\end{document} then f is called a 2-rainbow dominating function (2RDF) of G. The weight w(f) of a function f is defined as w(f)=∑v∈V(G)f(v)\documentclass[12pt]{minimal}
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\begin{document}$$w(f)=\sum _{v\in V(G)}\left| f(v)\right| $$\end{document}. The minimum weight of a 2RDF of G is called the 2-rainbow domination number of G, denoted by γr2(G)\documentclass[12pt]{minimal}
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\begin{document}$$\gamma _{r2}(G)$$\end{document}. The 2-rainbow domination stability, stγr2(G)\documentclass[12pt]{minimal}
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\begin{document}$$st_{\gamma r2}(G)$$\end{document}, of G is the minimum number of vertices in G whose removal changes the 2-rainbow domination number. In this paper, we first determine the exact values on 2-rainbow domination stability of some special classes of graphs, such as paths, cycles, complete graphs and complete bipartite graphs. Then we obtain several bounds on stγr2(G)\documentclass[12pt]{minimal}
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\begin{document}$$st_{\gamma r2}(G)$$\end{document}. In particular, we obtain stγr2(G)≤δ(G)+1\documentclass[12pt]{minimal}
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\begin{document}$$st_{\gamma r2}(G)\le \delta (G)+1$$\end{document} and stγr2(G)≤|V(G)|-Δ(G)-1\documentclass[12pt]{minimal}
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\begin{document}$$st_{\gamma r2}(G)\le |V(G)|-\varDelta (G)-1$$\end{document} if γr2(G)≥3\documentclass[12pt]{minimal}
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\begin{document}$$\gamma _{r2}(G)\ge 3$$\end{document}. Moreover, we prove that there exists no graph G with stγr2(G)=|V(G)|-2\documentclass[12pt]{minimal}
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\begin{document}$$st_{\gamma r2}(G)=|V(G)|-2$$\end{document} when n≥4\documentclass[12pt]{minimal}
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\begin{document}$$n\ge 4$$\end{document} and characterize the graphs G with stγr2(G)=|V(G)|-1\documentclass[12pt]{minimal}
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\begin{document}$$st_{\gamma r2}(G)=|V(G)|-1$$\end{document} or stγr2(G)=|V(G)|-3\documentclass[12pt]{minimal}
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\begin{document}$$st_{\gamma r2}(G)=|V(G)|-3$$\end{document}.
