Bifractional Brownian motion (bfBm) is a centered Gaussian process with covariance. R( H,K) ( s,t) = 2 − K((| s| 2 H + | t| 2 H) K − | t − s| 2 HK), s,t ∈ ℝ We study the existence of bfBm for a given pair of parameters ( h, k) and encounter some related limiting processes.