The allometric-autoregressive model describes growth accurately and is useful in the characterization of growth responses. Hence, the potential of the model for selection was investigated. Rats were used in a selection experiment, where selection was practised for slope (b) and intercept (In a) of the allometric function: w = In a + bv [where w = In (body mass) and v = In (cumulative feed intake)], and for p, the autoregression slope of In (cumulative feed intake). Facilities for five selection groups of 40 rats each were available. Both upward and downward within-family selections were practised for In a and b, and only downward selection for p. In the medium-term, the observed direct responses to selection for parameters of the allometric-autoregressive model were irregular, and there was a marked discrepancy between the observed and expected responses. It was postulated that poor fit of the model in later generations, a lack of genetic variance, mutation, genetic drift and / or natural selection may be causing these discrepancies. The selection responses were accompanied by losses of fitness during certain generations, while in others, the responses disappeared altogether. In certain generations, however, fitness was regained and this was followed by renewed appearance of responses. This pattern of response points to the presence of natural selection, which was corroborated by the differences between the effective and expected selection intensities. It was concluded that the slope of the allometric function seems to be the only parameter worth considering as a selection criterion.