Nowadays, memristors are of considerable interest to researchers and engineers due to the promise they hold for the creation of power-efficient memristor-based information or computing systems. In particular, this refers to memristive devices based on the resistive switching phenomenon, which in most cases are fabricated in the form of metal–insulator–metal structures. At the same time, the demand for compatibility with the standard fabrication process of complementary metal–oxide semiconductors makes it relevant from a practical point of view to fabricate memristive devices directly on a silicon or SOI (silicon on insulator) substrate. Here we have investigated the electrical characteristics and resistive switching of SiOx- and SiNx-based memristors fabricated on SOI substrates and subjected to additional laser treatment and thermal treatment. The investigated memristors do not require electroforming and demonstrate a synaptic type of resistive switching. It is found that the parameters of resistive switching of SiOx- and SiNx-based memristors on SOI substrates are remarkably improved. In particular, the laser treatment gives rise to a significant increase in the hysteresis loop in I–V curves of SiNx-based memristors. Moreover, for SiOx-based memristors, the thermal treatment used after the laser treatment produces a notable decrease in the resistive switching voltage.