  We present a study of four muon, four electron, and two muon two electron
events using 1 fb^(-1) of data collected with the D0 detector at the Fermilab
Tevatron p-barp Collider at sqrt(s) = 1.96 TeV. Requiring the lepton pair
masses to be greater than 30 GeV, we observe one event, consistent with the
expected background of 0.13 +- 0.03 events and with the predicted standard
model ZZ and Z\gamma^* production of 1.71 +-0.15 events. We set an upper limit
on the ZZ and Z\gamma^* cross section of 4.4 pb at the 95% C.L. We also derive
limits on anomalous neutral trilinear ZZZ and ZZ\gamma^* gauge couplings. The
one-parameter 95%$ C.L. coupling limits with a form factor scale Lambda = 1.2
TeV are -0.28 < f_(40)^Z < 0.28, -0.31 < f_(50)^Z < 0.29, -0.26 < f_(40)^\gamma
< 0.26, and -0.30 < f_(5 0)^\gamma < 0.28.
