A process suitable for producing Josephson tunnel junction circuits using all-niobium nitride (NbN) refractory electrodes is described. In this process, an in situ-deposited trilayer film of NbN/MgO-Mg/NbN is used to fabricate the Josephson junctions. The barrier is formed by thermal oxidation of a thin magnesium (Mg) film sputtered from an Mg target. This process has produced NbN-based Josephson junctions with good tunneling characteristics for devices as small as 3 mu m(2). High quality tunnel junction devices have been achieved using this process, with energy gap voltages of nearly 5 mV. These devices exhibit characteristics similar to those of junctions fabricated with barriers deposited from a ceramic magnesium oxide (MgO) target. Thermally-oxidized magnesium barriers offer a higher degree of control over the tunnel barrier thickness, which results in a significant improvement over processes where the tunnel barrier is directly deposited from an MgO target. The application of this process to all-NbN-based circuits will also be discussed.