Using gr’-and g*-paramener equivalent resonators and expressing the beam radius on output mirror by normalized refractive power Dn and parameter A, the sufficient and necessa y conditions for dynamic stable telescopic-resonators in TEM00-mode operation is derived for the first time. Analytical expressions of normalized refractive power Dn, thermal local length, and g1*, g2* parameters of dynamic stable telescopic-resonators are deduced respectively. Eesults obtained in this work can be easily generalized to multi-element resonators with many internal lenses(one of which is a thermal lens).