Bifractional Brownian motions introduced by Houdre and Villa is an interesting family of self-similar Gaussian processes depending on two parameters H,K and reducing to the classical fractional Brownian motion when K=1. We study the existence of the bifractional Brownian motion for a given pair (H,K) and encounter some related limiting processes. Our main tool is the spectral analysis of appropriate fractional stationary processes. This is a joint work with Ksenia Volkova.