The present article develops a decentralized interbase station slot synchronization algorithm suitable for cellular mobile communication systems. The proposed cellular firefly synchronization (CelFSync) algorithm is derived from the theory of pulse-coupled oscillators, common to describe synchronization phenomena in biological systems, such as the spontaneous synchronization of fireflies. In order to maintain synchronization among base stations (BSs), even when there is no direct link between adjacent BSs, some selected user terminals (UTs) participate in the network synchronization process. Synchronization emerges by exchanging two distinct synchronization words, one transmitted by BSs and the other by active UTs, without any a priori assumption on the initial timing misalignments of BSs and UTs. In large-scale networks with inter-BS site distances up to a few kilometers, propagation delays severely affect the attainable timing accuracy of CelFSync. We show that by an appropriate combination of CelFSync with the timing advance procedure, which aligns uplink transmission of UTs to arrive simultaneously at the BS, a timing accuracy within a fraction of the inter-BS propagation delay is retained.