We performed a direct search for the anomalous ZZγ and Zγγ couplings by studying p¯p→ℓℓγ+X (ℓ=e,μ) events at √s=1.8 TeV with the D0 detector at the Fermilab Tevatron Collider. A fit to the transverse energy spectrum of the photon in the signal events, based on the data set corresponding to an integrated luminosity of 14.3pb−1 ( 13.7pb−1) for the electron (muon) channel, yields the following 95% confidence level limits on the anomalous CP-conserving ZZγ couplings: |hZ30|<1.8 ( hZ40=0) and |hZ40|<0.5 ( hZ30=0), for a form-factor scale Λ=500 GeV. Limits for the Zγγ couplings and CP-violating couplings are also discussed.Received 10 March 1995DOI:https://doi.org/10.1103/PhysRevLett.75.1028©1995 American Physical Society