Summary: If \(a(t)\) and \(b(t)\) are positive almost periodic functions, and \(K(t)\) is nonnegative and piecewise continuous on \([0, \infty)\), conditions under which the equation \[ N'(t)= N(t)\Biggl(a(t)- b(t) \int^\infty_0 K(s) N(t- s)ds\Biggr) \] has a positive almost periodic solution \(N^*(t)\) on \((- \infty, \infty)\) are given which attracts all other positive solutions as \(t\to a\). These conditions are quite explicit and apparently new.