We analyze and investigate experimentally the output stability and the frequency tuning characteristics of weakly triply resonant silver gallium sulfide (AgGaS2) optical parametric oscillators. These oscillators are subject to thermally induced bistability and passive self-frequency-locking phenomena. The robust self-frequency-locking on a single-mode pair (thermal lock) originates from the material’s ability to correct external cavity-length perturbations, which would normally cause a mode hop, by increasing or decreasing the optical path length of the cavity through the thermo-optic effect triggered by the intracavity signal–idler power fluctuations. The Fourier frequency bandwidth of this passive servo is limited to ∼1 kHz by the thermal diffusion time constant, which is proportional to the ratio of the specific heat to the thermal conductivity Cp/Kc. A thermal feedback servo gain as high as 180 is obtained, owing to the large thermal figure of merit η=(dn/dT)/Kc of AgGaS2, leading to routine passive mode-hop-free operation for more than 30 min, without the need for an external cavity-length servo. Analysis of the stability range of the thermally loaded standing-wave resonator shows that thermal lensing is less critical for shorter doubly resonant optical parametric oscillator cavities employing shorter-curvature mirrors, in agreement with experimental observations. When a doubly resonant oscillator operates near the boundary of the power stability range a self-pulsing behavior is observed on a number of axial mode pairs. This self-pulsing is found to originate from the destabilization of a self-locked cw state, and the transition from self-pulsing to the stable self-frequency-locked state is found to be controlled by the pump frequency detuning. The passive stability allows the single-parameter frequency tuning to be studied. Under pure thermal lock operation the oscillators show a tendency to resist the pump frequency and temperature tuning processes. When an external cavity-length servo is implemented continuous tuning over 850 MHz, by means of the pump frequency tuning (Δνs/Δνp≈0.66), and over 100 MHz, by means of the crystal temperature (Δνs/ΔT≈250 MHz/°C), is obtained. These tuning ranges are in good agreement with calculations based on a cold doubly resonant oscillator.