Despite decades of studies on the grand problem of the glass transition the question of well-defined universal patterns, including the key problem of the previtreous behavior of the primary (structural) relaxation time, remains elusive. This report shows the universal previtreous behavior of the apparent fragility, i.e. the steepness index m P ( T > T g ) = d log 10 τ( T)/ d( T g / T). It is evidenced that m P ( T) = 1( T − T*), for T → T g and T*= T g − Δ T*. Basing on this finding, the new 3-parameter dependence for portraying the previtreous behavior of the primary relaxation time has been derived: τ( T) = C Ω(( T − T*)/ T) −Ω × [ exp(( T − T*)/ T)] Ω. The universality of obtained relations is evidenced for glass formers belonging to low molecular weight liquids, polymers (melt and solid), plastic crystals, liquid crystals, resins and relaxors. They exhibit clear preferences either for the VFT or for the critical-like descriptions, if recalled already used modeling. The novel relation can obey even above the dynamic crossover temperature, with the power exponent Ω ranging between ~17 (liquid crystals) to ~57 (glycerol), what may indicate the impact of symmetry on the previtreous effect. Finally, the emerging similarity to the behavior in the isotropic phase of nematic liquid crystals is recalled.