In the first part of this paper the author obtains new sufficient conditions for global attractivity in nonlinear delay differential equations using a mixed monotone technique. The equations considered include the equation of the form \((1)\quad (d/dt)[x(t)-ax(t-\tau)]=-\mu x(t)-bx(t-\sigma)+f(x(t-\gamma)),\) where a, b, \(\mu\), \(\tau\), \(\sigma\), and \(\gamma\) are nonnegative numbers such that \(a\in [0,1)\), \(b+\mu >0\) and \(\lambda (1-ae^{-\lambda \tau})=-\mu -be^{-\lambda \sigma}\) has a negative root; moreover f(x) is a mixed monotone function, that is, \(f(x)=\omega (x,x)\), where \(\omega\) (x,y) is monotone decreasing in x and increasing in y. In the second part of this paper the author generalizes the above result for some delay differential equations which contain (1), and in the third part he applies his results to some equations from mathematical biology.