The authors study properties of a nonautonomous competitive Lotka-Volterra system for two spieces \(u\) and \(v\) of the form \[ u'=u(\lambda-a(t)u-bv),\;v'=v(\mu-cv-du). \] They also consider the “pullback” asymptotic behaviour and the describe the behaviour both as \(t\to\infty\) and \(t\to-\infty\).