Polycrystalline U(Ni1-xCux)(2)Si-2 solid solutions have a tetragonal ThCr2Si2 type crystal structure. Antiferromagnetic (AF) transitions, observed by measurements of a.c. susceptibility for x=0.10, 0.25, and 0.50, are confirmed by neutron diffraction. The AF structures are of type I (+-+-) with k=(0,0,1) below T-0=108+/-5 K for x=0.10 (with a possible incommensurate phase at 108-135 K), T-N=151+/-3 K for x=0.25, and T-N=150+/-2 K for x=0.50. The a.c. susceptibility transition for x=0.75 is associated with the three magnetic structures observed by neutron diffraction: AF I, ferrimagnetic (++-) and AF IA (++--), with k=(0,0,1), (0,0,2/3) and (0,0,1/2), and T-N=120+/-3, 115+/-4 and 110+/-3 K respectively. Including previous neutron results on single-crystal UNi2Si2 and powdered UCu2Si2, a magnetic phase diagram of the U(Ni1-xCux)(2)Si-2 system is proposed and discussed.