We have performed elastic and inelastic neutron scattering experiments on solid solutions of U(Ru1-xRhx)(2)Si-2 with Ru-rich concentrations: x = 0, 0.01, 0.02, 0.025, 0.03, 0.04 and 0.05. Hidden order is suppressed with increasing x, and correspondingly, the onset temperature T-m (similar to 17.5 K at x = 0) of weak antiferromagnetic (AF) Bragg reflection decreases. For x = 0.04 and 0.05, no magnetic order is detected in the investigated temperature range down to 1.4 K. In the intermediate range, 0.02 less than or equal to x less than or equal to 0.03, We found that the AF Bragg reflection is strongly enhanced. At x = 0.02, this enhancement takes place at similar to7.7 K (drop T-M), which is significantly lower than T-m (similar to 13.7 K). T-M increases with increasing x, and seems to merge with T at x = 0.03. If the AF state is assumed to be homogeneous, the staggered moment mu(0), estimated at 1.4 K increases from 0.02(2) mu(B)/U (x = 0) to 0.24(l) mu(B)/U (x = 0.02). The behavior is similar to that observed under hydrostatic pressure (mu(0) increases to similar to0.25 mu(B)/U at 1.0 GPa), suggesting that the AF evolution induced by Rh doping is due to an increase in the AF Volume fraction. We also found that the magnetic excitation observed at (1, 0, 0) below T-m disappears as T is lowered below T-M.