Rank statistics to test the null hypothesis that X and Y are conditionally, given Z, independent are given and their asymptotic properties are investigated under the model (X, Y, Z) = (U+ anW, V-FbnW,W) where (U, V) and W are independent. It is shown that linear rank tests given by (X, Y) based on the random sample of size n are asymptotically distribution-free when (an,bn)=n-'12(a,b). It is also shown that Spearman's coefficient of rank correlation and Kendall's coefficient of rank correlation given by (X—czZ, Y—oZ) are asymptotically distribution-free when (an,bn)=(a,b) where (a,b)is some consistent estimator of (a,b).