The author’s standpoint regarding the category definition of “higher education institution competitiveness” is given in the paper. The most important characteristic of the general higher education institution competitiveness is defined as satisfaction of internal stakeholders—employees, achieved by means of implementing two directions: meeting employees’ needs in decent working conditions; meeting needs of external stakeholders to the fullest extent allowing personnel to be proud of belonging to a higher education institution. The authors revealed and systematized the factors influencing the level of higher education institution competitiveness. The methodological ideas on higher education institution competitiveness are considered and the authors’ technique of a higher education institution competitiveness assessment in educational services markets, scientific research and development, labor and general competitiveness including the following stages is presented: our opinion is that on the whole the technique of a higher education institution competitiveness assessment is to include the following stages: indicators formation of higher education institution competitiveness assessment and their classification according to competitiveness types; indicator distribution of a higher education institution competitiveness assessment in preference manner; an indicator assessment on the basis of the subjective and objective approach; an integrated indicator assessment of higher education institution competitiveness (the general one and by types of competitiveness). The need for use of the subjective and objective approach to a higher education institution competitiveness assessment is proved.