We report on the analysis of the rare decay K-L--> mu (+)mu (-)gamma the 19
97 data from the KTeV experiment at Fermilab. A total of 9327 candidate eve
nts are observed with 2.4% background, representing a factor of 40 increase
in statistics over the current world sample. We find that B(K-L --> mu (+)
mu (-)gamma) = (3.62 +/-0.04(stat)+/-0.08(syst)) x 10(-7). The form factor
parameter alpha (K*) is measured to be alpha (K*) = -0.160(-0.028)(+0.026).
In addition, we make the first measurement of the parameter alpha from the
D'Ambrosio-Isidori-Portoles form factor, finding alpha = -1.54 +/-0.10. In
that model, this alpha measurement limits the Cabibbo-Kobayashi-Maskawa pa
rameter rho > -0.2.