The purpose of this paper is to extend the newly established α- feasibility and α- efficiently concept for grey flexible fuzzy linear programming, so as to present some important new concepts, models, methods, and a new framework of grey system theory in mathematical programming. In this paper, we concentrate on Grey Fuzzy Flexible Linear Programming (GFFLP) problems as a reasonable extension of GLP models that adapt more to real situations. For this aim, after defining the classical GFFLP model, we first introduce a new concept of α ̅-feasibility and α ̅- efficiency to these problems, and then we propose a two-phase approach to solve the mentioned problems. Furthermore, we give some fundamental theorems and constructive results to support and verify the proposed solving process. This approach will be open a new window to the modeling of the problems in the real world under flexibility conditions. A lot of successful practical applications of the new models to solve various problems have been found in many different areas and disciplines such as agriculture, decision sciences, diet problem, ecology, economy, geology, earthquake, industry, material science sports, medicine, management, transportation, and etc. Because of the ability to deal with poor, incomplete, or uncertain problems with grey systems, most real-world processes in decision problems are in the grey stage due to lack of information and uncertainty. However, the flexibility assumption in decision making is more comfortable for the Decision Maker (DM), hence in this paper, we concentrate on Grey Fuzzy Flexible Linear Programming (GFFLP) problems as a reasonable extension of GLP models in which is more adept with the real situations, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially when the available information is incomplete and the collected data is inaccurate. In this study, a general picture of grey mathematical programming under flexibility conditions is given as a new model and a new framework for various real problems where partial information is known; especially for uncertain decision systems with few data points and poor information.