Let \(\{X_ t\}\) be a stationary Gaussian sequence with \(EX_ t=0\) and with a spectral density \(f_{\theta}(\lambda)\), where \(\theta\in \Theta\subset R_ p\). Denote \(P(n,f_{\theta})\) the Gaussian distribution of \(X_ 1,...,X_ n\). The author proves that under suitable conditions the family \(\{P(n,f_{\theta})\}\) is locally asymptotically normal. It means that for a given \(\theta_ 0\in\Theta \) there exists a regular matrix \(\Gamma_{\theta_ 0}\) such that for every \(u\in R_ p\) \[ \ln (dP(n,f_{\theta_ 0+n}-1/2_ u)/dP(n,f_{\theta_ 0}))= u'\Delta_{n,\theta_ 0}- (1/2)u'\Gamma_{\theta_ 0}u+\Phi_ n(u,\theta_ 0), \] where \(\Delta_{n,\theta_ 0}\) has asymptotically \(N(0,\Gamma_{\theta_ 0})\) distribution and \(\Phi_ n(u,\theta_ 0)\to 0\) in probability as \(n\to\infty \).