Distributional studies and regression models have played important roles in statistical analysis of circular data. Asymmetric circular-linear multivariate regression models (SenGupta and Ugwuowo Environ. Ecol. Stat. 13(3), 299-309 2006) are motivated by and applied to predict some environmental characteristics based on both circular and linear predictors. In this paper, we consider a likelihood approach (Cook J. R. Stat. Soc. Ser. B Stat Methodol. 48(2), 133-169 1986) to study influence diagnostic analysis for these models, using the maximum likelihood estimation and influence diagnostics methods. The observed information matrices and normal curvatures are derived. Simulated and real data examples are then provided to illustrate our approach and establish the utility of our results.