Exchange coupling has been studied on fine particles of Co with 35 at.% Ni which are surface oxidized to have an antiferromagnetic Co-Ni monoxide shell. Cooling a sample in the state of remanence through the Néel-temperature of the monoxide, a hysteresis loop is observed which is shifted along the field axis. A field of loop displacement is defined with respect to remanence coercivity as

. It is found to be quantitatively equivalent to an external field in the anhysteretic magnetization process which occurs if a superimposed alternating field is slowly decreased to zero from a large initial value. An universal curve is obtained by plotting

, the normalized anhysteretic remanent magnetization in zero external field, as a function of

, where

is the anhysteretic susceptibility at

and

is the saturation remanent magnetization. The curve is valid for all combinations of

and

. The consequences for recording on a tape containing the above particles are discussed.