Two scries of simulation experiments were used to investigate the accuracy of treatment and variance estimation with a neighbour analysis of field trials proposed by Gleeson & Cullis (1987). The first series examined the accuracy of residual maximum likelihood (REML) estimation of seven theoretical error models applicable to field trials. REML estimation provided accurate estimates of the variance parameters, but the Ftest of treatments was slightly biased upward (to +2·4%) for first differences models and slightly biased downwards (to –1·4%) for second differences models. The second series of simulations, based on 19 uniformity data sets, illustrated that treatment effects were consistently estimated more accurately by the REML neighbour (RN) analysis of Gleeson & Cullis (1987) than by incomplete block (IB) analysis with recovery of interblock information. The relative gain in accuracy of RN over IB depends on the amount of systematic variation or ‘trend’ in the trial, and ranged from 6 to 18% with an average of 12% for a range of trend and error variances commonly encountered in field trials. The predicted average standard errors of pairwise treatment differences from the RN analysis were in close agreement with their empirical estimates, indicating that the predicted average S.E.D. is approximately valid.