Let {zeta((k))(m,k) (t), t >= 0}, k > 0 be random processes defined as the differences of two independent stationary chi-type processes with m and k degrees of freedom. In this paper we derive the asymptotics P{sup(t is an element of[0,T]) zeta((k))(m,k)(t) > u}, u -> infinity under some assumptions on the covariance structures of the underlying Gaussian processes. Further, we establish a Berman sojourn limit theorem and a Gumbel limit result.