Summary: A property \(P\) defined on all graphs of order \(n\) is said to be \(k\)-stable if for any graph of order \(n\) that does not satisfy \(P\), the fact that \(uv\) is not an edge of \(G\) and that \(G+ uv\) satisfies \(P\) implies \(d_G(u)+ d_G(v)< k\). Every property is \((2n-3)\)-stable and every \(k\)-stable property is \((k+1)\)-stable. We denote by \(s(P)\) the smallest integer \(k\) such that \(P\) is \(k\)-stable and call it the stability of \(P\). This number usually depends on \(n\) and is at most \(2n-3\). A graph of order \(n\) is said to be pancyclic if it contains cycles of all lengths from \(3\) to \(n\). We show that the stability \(s(P)\) for the graph property ``\(G\) is pancyclic'' satisfies \(\max(\lceil{6n\over 5}\rceil- 5,n+ t)\leq s(P)\leq \max(\lceil{4n\over 3}\rceil -2, n+t)\), where \(t= 2\lceil{n+ 1\over 2}\rceil- (n+ 1)\).