EUV structures in the solar atmosphere are studied on the basis of the energetically open equivalent circuits. The systems consist of current carrying magnetic loops that interconnect a high ¿ energy-production region with a low ¿ dissipation region and include the transition region where the most efficient generation of currents and transport of the accumulated energy through the resistive stresses occurs. As nonconservative systems with a source and sink of energy, they may be driven into various dynamic forms via nonlinear processes with continuous flow of matter and energy. The corresponding equivalent circuit equation has the form of the Van der Pol oscillator. Depending on the coefficients determined by the system parameters, this equation describes different behaviors of the EUV structures including long-living steady loops with subtle oscillations, loops in the relaxation regime, and the periodically flaring and exploding loop systems. The model predicts that the EUV loops must have a filamentary structure and allows us to estimate the limiting currents and critical radii of elemental filaments associated with the stability criteria. Simple relations between the parameters, most of which are observables, may provide reliable diagnostic tools.