This study focused on organizational core issues and strategic implementation in public tertiary institutions in Nigeria. A survey research design was adopted with mixed instruments of questionnaire and interview; primary data were gathered through the administration of 94 copies of the questionnaire instrument combined with in-depth interviews with 6 administrators of the studied organizations; purposive sampling was used for data collection. Descriptive analytical tools were used to analyze data profile. Inferential statistics, correlation analysis and multiple regression analysis were used to test research hypothesis. The results revealed that the application of strategic management by these institutions is still at its infancy. The study also revealed that organizational issues, namely leadership (Beta=.301, t=3.071, p<0.05) organizational structure (Beta=.213, t=2.766, p<0.05), organizational culture (Beta=.323, t=3.845, p<0.05) and resource allocation (Beta=.233, t=2.427, p<0.05) had significant positive influence on strategic implementation in public tertiary institutions in Nigeria. It was recommended that managements of public tertiary institutions in Nigeria should benchmark the strategic management practices of their peers in the developed economy in guiding their administration; that the capacity of administrators of these institutions be strengthened through relevant exposure and training in strategic management; that in view of the significant positive influence of organizational issues on strategic implementation, these variables should be properly managed to achieve comparative advantage.