It has been recently shown that Generative Adversarial Networks (GANs) can produce synthetic images of exceptional visual fidelity. In this work, we propose the first GAN-based method for automatic face aging. Contrary to previous works employing GANs for altering of facial attributes, we make a particular emphasize on preserving the original person's identity in the aged version of his/her face. To this end, we introduce a novel approach for "Identity-Preserving" optimization of GAN's latent vectors. The objective evaluation of the resulting aged and rejuvenated face images by the state-of-the-art face recognition and age estimation solutions demonstrate the high potential of the proposed method.