Hysteretic SIS and SNS Josephson junction devices have been fabricated from epitaxial thin film structures. The superconductor-insulator-superconductor (SIS) tunnel junctions were made of BKBO thin film electrodes and a KNbO3 barrier. Tunnel structure with gap voltages as high as 8 mV and switching voltages as high as 5 mV have been demonstrated. Near ideal SIS tunnel characteristics for HTS thin film trilayer structures are reported for the first time. Zero bias currents are modulated by small magnetic fields and Shapiro steps are observed under rf-irradiation. Superconductor-normal metal-superconductor (SNS) devices made from a YBCO bottom thin film electrode, a SrTiO3 barrier, and a top BKBO film possessed McCumber parameters in excess of 100 and displayed IcR products up to 1 mV at 4.2 K.