In this article, we consider flexible seasonal time series models which consist of a common trend function over periods and additive individual trend (seasonal effect) functions. The consistency and asymptotic normality of the local linear estimators were obtained under the $α$-mixing conditions and without specifying the error distribution. We develop these results to consistency and asymptotic normality of local linear estimates by using central limit theorems for flexible seasonal time series model, which error terms are $k$-weak dependent and $λ$-weak dependent random variables.