AbstractConsider an experiment where a nonlinear continuous functional relationship exists betweenyandX.Assume that this relationship has been measured atnreplicated points ofXfrom each ofttreatments or populations. Assume further that theXare fixed unknown vectors and that the location parametervis either a fixed unknown vector or a vector of random variables. In the first case various linear hypotheses are to be tested aboutv, such as tests for main effects and interaction; in the second case, the mean and variance of the random variablevare to be estimated. A two‐step procedure based on asymptotic theory is presented to test hypotheses or develop estimates for the fixed effects or random effects functional errors‐in‐variable model. An example of a one‐way random effects model i