ABSTRACT There is still a limited number of high-redshift (z > 3) active galactic nuclei (AGNs) whose jet kinematics have been studied with very long baseline interferometry (VLBI). Without a dedicated proper motion survey, regularly conducted astrometric VLBI observations of bright radio-emitting AGN with sensitive arrays can be utilized to follow changes in the jets, by means of high-resolution imaging and brightness distribution modelling. Here, we present a first-time VLBI jet kinematic study of NVSS J080518 + 614423 (z = 3.033) and NVSS J165844 − 073918 (z = 3.742), two flat-spectrum radio quasars that display milliarcsecond-scale jet morphology. Archival astrometric observations carried out mainly with the Very Long Baseline Array, supplemented by recent data taken with the European VLBI Network, allowed us to monitor changes in their radio structure in the 7.6−8.6 GHz frequency band, covering almost two decades. By identifying individual jet components at each epoch, we were able to determine the apparent proper motion for multiple features in both sources. Apparent superluminal motions range $(1-14)\, c$, and are found to be consistent with studies of other high-redshift AGN targets. Using the physical parameters derived from the brightness distribution modelling, we estimate the Doppler-boosting factors (δ ≈ 11.2 and δ ≈ 2.7), the Lorentz factors (Γ ≈ 7.4 and Γ ≈ 36.6), and the jet viewing angles (θ ≈ 4.4° and θ ≈ 8.0°), for NVSS J080518 + 614423 and NVSS J165844 − 073918, respectively. The data revealed a stationary jet component with negligible apparent proper motion in NVSS J165844 − 073918.