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We say that a class F consisting of analytic functions f (z)=∑ n= 0∞ a n z n in the unit disk D:={z∈ C:| z|< 1} satisfies a Bohr phenomenon if there exists r f∈(0, 1) such that∑ n= 1∞| a n z n|≤ d (f (0),∂ f (D)) for every function f∈ F and| z|= r≤ r f, where d is the Euclidean distance. The largest radius r f is the Bohr radius for the class F. In this paper, we establish the Bohr phenomenon for the classes consisting of Ma-Minda type starlike functions and Ma-Minda type convex functions as well as for the class of starlike functions with respect to a boundary point.