Let $\xi(t)=\theta(t)+\Delta(t)$ where $\Delta(t)$ is a stationary «noise» process, $\theta(t)$ is a «signal» of the form (4$'$) (the numbers $\lambda_k$ satisfy (5)). In the paper, an estimation problem is considered for an arbitrary bounded linear functional $\varphi(\theta)$. Asymptotical expressions are obtained for the variances of the leastsquares estimators and best unbiased ones. The main result is: Let the spectral density $f(\lambda)$ of the process $\Delta(t)$ satisfy (6), be uniformly bounded on $(-\infty,\infty)$ and continuous and positive at each point $\lambda_k$. Then the least-squares estimators are asymptotically effecient. As an example, the least-squares estimators of a periodic signal are considered.