We introduce the notions of the asymptotic ？-sequence with respect to the stronger Meir-Keeler cone-type mapping ∶int()∪{}→[0,1) and the asymptotic ？-sequence with respect to the weaker Meir-Keeler cone-type mapping ∶int()∪{}→int()∪{} and prove some common fixed point theorems for these two asymptotic sequences in cone metric spaces with regular cone . Our results generalize some recent results.