In the itinerant electron theory of antiferromagnetism one postulates that the Fermi surface of the metal has two sheets which can be brought into point-by-point fit by a translation in the crystal momentum space. The wave vector of the spin-density wave corresponds to the amount of translation. In real metals the pieces of Fermi surface do not nest exactly. We have explored some consequences of imperfect Fermi-surface nesting on the basis of a one-band model. We find that there exists a minimum value of the interaction strength below which antiferromagnetism does not occur; and when antiferromagnetism does occur the ratio 2Δ0/kTN is always greater than 3.5. These results were also obtained in more elaborate model of Kimball and Falicov. However, in contrast to Kimball and Falicov, we find a second-order phase transition at TN. This is perhaps due to the oversimplification of our model. If the exchange interaction is not strong enough to stabilize antiferromagnetism, the result is a nearly antiferromagnetic material in which a new type of paramagnon may be found. Some physical properties of these virtual modes are discussed.