Oblique bifactor models, where group factors are allowed to correlate with one another, are commonly used. However, the lack of research on the statistical properties of oblique bifactor models renders the statistical validity of empirical findings questionable. Therefore, the present study took the first step to examine the statistical properties of oblique bifactor models through Monte Carlo simulations. Study 1 showed that the classic oblique bifactor "measurement" models had severe convergence issues in many conditions. Even for converged replications, both factor loading and group factor correlation estimates were severely biased. Study 2 further showed that the classic oblique bifactor "predictive" models still had serious convergence problems, and structural parameters suffered from issues of severe estimation bias and low power. Fortunately, the augmentation approach, where one or multiple indicators are specified to load onto only the general factor but not any of the group factors, was useful in ameliorating these issues in both oblique bifactor measurement and predictive models. Tentative recommendations regarding the selection between oblique and orthogonal bifactor models and the approaches to finding augmenting indicators were provided.