We consider near-threshold a 0 (980)-meson production in πN and N N collisions. An effective Lagrangian approach with one-pion exchange is applied to analyze different contributions to the cross section for different isospin channels. The Reggeon exchange mechanism is also evaluated for comparison. The results from πN reactions are used to calculate the contribution of the a 0 meson to the cross sections and invariant KK mass distributions of the reactions pp → pnK +K 0 and pp → ppK + K − . It is found that the experimental observation of a + 0 mesons in the reaction pp → pnK +K 0 is much more promising than the observation of a 0 0 mesons in the reaction pp → ppK + K − . Effects of isospin violation in the reactions pN → da 0 , pd → 3 He/ 3 H a 0 , and dd → 4 He a 0 , which are induced by a 0 (980)f 0 (980) mixing, are also analyzed.