Neutron-diffraction results on Zn(x)Co(1-x)FeCrO4 (x = 0.45, 0.50, and 0.55) and ac susceptibility measurements are described. Neutron measurements were extended down to 6 K for the x = 0.50 compound to check the magnetic structure associated with the phase transition seen in X(ac) around 20 K for the x greater-than-or-equal-to 0.50 compounds. For Zn ion concentration greater than 0.45, the broad distribution of X(ac) and the sluggish behavior of the ordered magnetic moment in the temperature range 300 greater-than-or-equal-to T greater-than-or-equal-to 100 K suggest the presence of finite magnetic clusters coexisting with the infinite magnetic network. For all the compositions, considerable reduction in the B-site moment and the absence of the (200) magnetic reflection confirm that the system is not a conventional ferrimagnet. The most interesting feature is the appearance of a diffuse hump at a Q value corresponding to the (200) reflection for x = 0.50, indicating the buildup of short-range correlation of the transverse components of the B-site moments. On further lowering the temperature, the intensity of the fundamental Bragg reflection decreases below 10 K, while the diffuse hump persists. A qualitative explanation of all these observed features is given in light of theoretical ideas on random magnetic systems.