Let BH, K={BH, K(t), t \in R +} be a bifractional Brownian motion in R d. We prove that BH, K is strongly locally non-deterministic. Applying this property and a stochastic integral representation of BH, K, we establish Chung's law of the iterated logarithm for BH, K, as well as sharp Hölder conditions and tail probability estimates for the local times of BH, K. We also consider the existence and regularity of the local times of the multiparameter bifractional Brownian motion BH̅, K̅={BH̅, K̅(t), t \in R +N} in R d using the Wiener–Itô chaos expansion.