Under certain circumstances a superconducting ring containing a weak superconducting junction (a so called Superconduding Quantum Interference Device, a SQUID) has two metastable magnetic flux states separated by a potential barrier when an external magnetic field is applied of appropriate strength. If the junction has a small capacitance, at low temperatures where kT is very much smaller than the barrier height ΔU intrinsic magnetic flux transitions are observed from one metastable flux state into another and vice versa, or in other words a weak "persistent supercurrent" switches stochastically from one direction into the opposite. This flux transition mechanism at very low temperatures might be interpreted as due to macroscopic quantum tunnelling, a new macroscopic quantum effect.1,2)