For　the　general　unsteady　multi-dimensional　flow,　the　non-linear　non-equilibrium　nature　of　shock　waves　is　investigated　from　the　geometric　singular　perturbation　theory.　With　the　introduction　of　a　pressure　non-equilibrium　term,　the　modified　Euler　equation　can　be　reduced　to　systems　of　ordinary　differential　equations(ODEs)　along　carefully　constructed　curves.　Along　each　curve,　a　slow-fast　system　is　derived　from　the　governing　ODEs,　and　the　geometric　singular　perturbation　theory　is　then　applied.　The　motion　of　the　slow-fast　system　is　decomposed　to　two　parts,　the　quasi-equilibrium　slow　motion　where　the　non-equilibrium　effect　is　negligible　and　the　fast　motion　where　the　non-equilibrium　effect　plays　a　dominating　role.　It　is　then　shown　that　a　shock　wave　can　be　recognized　as　the　fast　motion　of　a　slow-fast　system　in　an　objective　manner,　and　this　shock　detection　method　can　serve　as　a　rational　foundation　for　practical　shock　detection　problem.　(C)　2018　Elsevier　B.V.　All　rights　reserved.