High temperature electrolysis based on solid oxide electrolysis cells (SOECs) is a promising technology for energy storage and synthetic fuel production. In recent years extensive efforts have been devoted to improving performance and durability of SOEC cells and stacks. Due to historical reasons and the convenience of doing constant current tests, (almost) all the reported SOEC tests have been galvanostatic. In this work, we report test results on two types of SOEC cells operated for electrolysis of steam in potentiostatic mode at 1.29 V. Both cells are Ni/YSZ fuel electrode supported type with different oxygen electrodes. The two cells exhibited different initial performance and different long-term degradation behavior. Detailed impedance analysis indicates that degradation happened mainly at the Ni/YSZ electrode for both cells. Large overpotential on the Ni/YSZ electrode was identified as the main cause of the degradation. Operation strategies were further proposed for electrolysis operation in potentiostatic mode.