Summary: In this paper we study the initial value problem of first order nonlinear differential equations with maxima and discuss the existence and approximation of the solutions. The main result relies on the Dhage iteration method embodied in a recent hybrid fixed point theorem of B. C. Dhage [Tamkang J. Math. 45, No. 4, 397–426 (2014; Zbl 1343.45004)] in a partially ordered normed linear space. At the end, we give an example to illustrate the hypotheses and applicability of the abstract results of this paper.