In many fields of applied mathematics, engineering and economic sciences there appear matrix Riccati equations. During the last three decades, there was achieved great progress in the mathematical theory of Riccati equations and its applications, with emphasis on Control Systems and differential games. Symmetric Riccati equations play a central role in optimal control, whereas non-symmetric matrix Riccati equations show up for instance in the theory of dynamic games. In this talk, we study the minimal non-negative solution of the Non-Symmetric Algebraic Riccati Equation (NARE) which has applications in transport theory and Markov models.