This paper introduces a two-timescale antenna position optimization framework for the pinching-antenna system (PASS). The proposed framework exploits statistical channel state information (CSI) to determine large-timescale pinching-antenna (PA) positions over the entire waveguide, and utilizes instantaneous CSI to refine PA positions at the small timescale within a local region. This approach effectively captures the benefits of large-timescale PA positioning for long-term system performance and small-timescale PA movement for real-time adaptation to fast channel fluctuations. For the single-user case, we derive closed-form solutions for the optimal large-timescale PA positions, and further analyze a performance upper bound together with the conditions for achieving this bound, which guide the small-timescale position refinement. For the multi-user case, an upper bound on the minimum rate among all users is derived. To maximize their minimum rate, we develop an element-wise search algorithm for large-timescale PA positioning and a projected gradient ascent method for small-timescale position refinement. Simulation results show that the proposed scheme closely approaches the derived bounds and consistently outperforms conventional schemes by reducing path loss via large-timescale PA positioning and suppressing inter-user interference through small-timescale local movement.

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