Improvement in efficiency and reliability are essential for more intensive deployment and commercial exploitation of solid oxide fuel cell (SOFC) systems. Apart of advancement in fabrication of new materials and stack designs, there emerges a strong need for innovative control strategies capable of balancing maximal stack life and efficiency of power conversion in a trade-off manner. Reliable online estimation of stack health and prediction of the remaining useful life (RUL) play a key role in new generation of SOFC control systems. In most works until today, the authors utilize voltage as a health index and based on that predict the RUL. Unfortunately, such an approach becomes inappropriate when the SOFC is operating under varying load conditions and, in particular, when the SOFC ages. In this paper, we propose a novel hybrid approach to RUL prediction of SOFC systems, which overcomes the limitations of the known approaches and allows for reliable RUL prediction in non-stationary operating conditions. The approach consists of three main parts, executed continuously online: (i) estimation of area specific resistance (ASR) of the stack, (ii) prediction of its future progress based on collected data, and (iii) prediction of RUL. The methodology is evaluated on a 6 kW SOFC system.