NSolve[{2*x*(1 - x/y) - x^2/(0.1^2*y^2 + x^2), 
        3*y*(1 - y/(2.5*z)), 2  z*(1 - z) - 0.01*x*z^2/y}, {x, y, 
        z}]

2*x*(1 - x/y) - x^2/(0.1^2*y^2 + x^2)

3*y*(1 - y/(2.5*z))

2  z*(1 - z) - 0.01*x*z^2/y