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In this paper we present two results in $(2+1)$ gravity coupled to nonlinearelectrodynamics. First it is determined the general form of the electromagneticfield tensor in $(2+1)$ gravity coupled to nonlinear electrodynamics instationary cyclic spacetimes. Secondly, it is determined a family of exactsolutions in $(2+1)$ gravity sourced by a nonlinear electromagnetic field. Thesolutions are characterized by five parameters: mass $M$, angular momentum $J$,cosmological constant $\Lambda$ and two electromagnetic charges, $q_{\alpha}$and $q_{\beta}$. Remarkably, the solution can be interpreted as a traversablewormhole, provided the fulfillment of certain inequalities by thecharacteristic parameters; fine tunning of the cosmological constant leads toan extreme black hole, whereas by switching off one of the electromagneticcharges, we obtain the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole.

Black Hole-Wormhole transition in (2+1) Einstein -- anti-de Sitter Gravity Coupled to Nonlinear Electrodynamics