Biological invasion is one of the most serious environmental problems, especially on oceanic islands. The Ogasawara Islands (recently registered as a World Natural Heritage site) are also suffering from this problem. Then, eradication projects are ongoing. Several invasive species are known to dominate in recipient ecosystems (e.g. goats and rats). Eradication of such invasive species may disturb the nutrient cycle in the ecosystem. It may cause extinction of many native species. In order to conserve such species, we should evaluate possible eradication scenarios. Therefire, we constructed a mathematical model simulating the nutrient cycles in the ecosystem on an island of the Ogasawara Islands (Nakoudo-jima Island), and tried to evaluate several scenarios of eradication of invasive goats and rats. Results of simulations suggested 1) both goats and rats should be eradicated together; 2) the rat eradication effort should be intensive enough to eliminate rats; 3) the rat eradication effort should be continued until rats are completely eliminated.