For a sequence (cn) of complex numbers, the quadratic polynomials fcn:= z2 + cn and thesequence (Fn) of iterates Fn: = fcn o ... o fc1 are considered. The Fatou set F(cn) is defined as the set ofall z ∈ C: = C U {∞} such that (Fn) is normal in some neighbourhood of z, while the complement J(cn) ofF(cn) (in C) is called the Julia set. The aim of this paper is to study the stability of the Julia set J(c,n) in the case where (cn) is bounded. A problem put forward by Brück is solved.