  In this article, existence of the $k$-th order derivatives of local time $
\widehat{\alpha}^{(k)}(x,t)$ is considered for two d-dimensional fractional
Ornstein-Uhlenbeck processes $X^{H_1}_t$ and $\widetilde{X}^{H_2}_s$ with Hurst
parameters $H_1$ and $H_2$, respectively. Moreover, H$\hat{o}$lder regularity
condition of fractional Ornstein-Uhlenbeck process $X^{H}_t$ of local time
$\tilde{\alpha}^{(k)}(x,t)$ is obtained by some techniques using in Guo et al.
(2017) and in Lou et al. (2017).
