Using the general principle of linear prediction for autotetraploids in the absence of epistasis, we envisage different types of individual selection with truncation: mass selection, general combining ability selection, and selection on progenies from self fertilization. General expressions for the first cycle of selection are given. With the assumption that a locus effect can be neglected relative to the total variance, response to n cycles of selection can be predicted. Because of a dominance effect, the response will be curvilinear. The consequence of relaxation of selection is also envisaged. For all three selection procedures, after several cycles of random mating without selection, the genetic advance decreases rapidly towards an asymptotic value which is dependent only on the additive variance. Results for autotetraploids without epistasis are clearly analogous to Griffing's results for diploids with epistasis restricted to pairs of loci.