Recently, the detection of the neutral simplest all-nitrogen ring, cyclic-N-3 radical, has been realized via various techniques, which has led to numerous studies oil its structures, energetics, and spectroscopy. In particular, it has been postulated as a possible building block of high energy density materials. Yet, its intermolecular reactivity is poorly understood. In this paper, we for the first time studied the reactions of cyclic-N3 with the widespread oxygen and water at the CCSD(T)/aug-cc-pVTZ //B3LYP/6-311 ++G(d,p)+ZPVE and G3B3// B3LYP/6-311++G(d,p) (italics) levels. An addition-elimination mechanism was revealed for the cyclic-N-3 + O-2 reaction that results in the elementary product N-2 + NO + O-3 with an overall barrier as high as 11.8 (11.0) kcal/mol. The calculated low rate constants (even at high temperatures) show that the cyclic-N-3 radical is stable against oxygen. The cyclic-N-3 + H2O reaction is associated with a quasi H-abstraction mechanism forming the product cyclic-N3H + OH with the rather high barrier of 35.7 (36.2) kcal/mol. This indicates that cyclic-N-3 is chemically inert toward H2O. Chemical implications of the present work are discussed.