  We consider stochastic differential equations dY=V(Y)dX driven by a
multidimensional Gaussian process X in the rough path sense. Using Malliavin
Calculus we show that Y(t) admits a density for t in (0,T] provided (i) the
vector fields V=(V_1,...,V_d) satisfy Hoermander's condition and (ii) the
Gaussian driving signal X satisfies certain conditions. Examples of driving
signals include fractional Brownian motion with Hurst parameter H>1/4, the
Brownian Bridge returning to zero after time T and the Ornstein-Uhlenbeck
process.
