A calculation is presented which describes the behaviour of a superconducting ring, containing one, respectively two weak links, with respect to the entry of applied magnetic flux. The case that no bias current is applied is considered, specially in the region of small critical current. Both situations are compared with each other and it will be shown that some important differences exist. In contrast to a single weak-link device, a symmetric double weak-link device exhibits hysteresis for all values of its critical current. The given calculations show that the double weak link system jumps from one flux state to another when the total embraced magnetic flux is equal to ( n + 1 2 .Φ 0( n = 0, 1, 2,....).