A thermal protection function (thermal disconnector) is usually built into voltage clamping-type surge protective devices (SPDs) such as metal oxide varistors (MOVs) for electric power. In addition, if excess voltage or degradation of an SPD causes a large fault current flow, an overcurrent protection function (current disconnector) is used. Thermal disconnectors and current disconnectors are collectively known as SPD disconnectors. IEC 61643–1 specifies the operation of SPD disconnectors when the AC current flowing to an SPD due to degradation failure is below 1A. In such cases, the operation of the thermal disconnector is usually checked. However, there is no concrete examination standard for the shut-off characteristics of a current disconnector. As for thermal disconnectors and current disconnectors, it is desirable that they both perform the shut-off operation and maintain proper functioning. In this study, we describe the operations of thermal and current disconnectors as they relate to SPD safety, with a particular focus on SPD failure causing a fault current exceeding 1A (AC) to flow to the SPD. We used a current fuse uniquely developed at our company and a circuit-breaker (MCCB) that is generally recommended by SPD manufacturers for the current disconnectors. The results of our investigation led us to propose a suitable shut-off characteristic for current disconnectors.