The content, morphology, and structure of precipitated wax crystals are major factors affecting crude oil rheology. In this paper, model oils obtained by dissolving a realistic mixture of long-chain n-octacosane in diesel fuels were studied using terahertz time-domain spectroscopy (THz-TDS) and microscopy to gain insight into clusters composed of asphaltene and wax with increasing wax content. The fractal dimension was used for quantitative characterization of the morphology and structure of clusters in the model oils. From the measured absorption and extinction coefficients in the THz region, dynamic processes of the clusters in the model oils were analyzed and identified. The extinction coefficient in the THz region strongly depended on the dispersed and aggregated states of the asphaltene and wax crystals. These observations suggest that the aggregation state of the particles in model oils can be monitored with THz-TDS. In the future, THz-TDS technology may be used to effectively analyze particle dispersion or the aggregation state in crude oil and may thus be useful for rapid assessment of the effect of pour-point depressant on wax crystal aggregates.