  We introduce a new Gaussian process, a generalization of both fractional and
subfractional Brownian motions, which could serve as a good model for a larger
class of natural phenomena. We study its main stochastic properties and some
increments characteristics. As an application, we deduce the properties of
nonsemimartingality, H\"{o}lder continuity, nondifferentiablity, and existence
of a local time.
