Layered cobaltates YBaCo2O5 + x have been investigated in the oxygen concentration range 0.23 ≤ x ≤ 0.52. It has been revealed that the oxygen ordering plays the key role in the appearance of anomalies in temperature dependences of structural parameters and electron transport. It has been shown that the orthorhombic lattice distortion caused by oxygen chain ordering is a necessary “trigger” for the phase transition from the insulating state to the metallic state at T ≈ 290–295 K, after which the orthorhombic distortion is significantly more pronounced. In the boundary region of the cobaltate compositions, where the oxygen ordering has a partial or local character, there are additional low-temperature (100–240 K) structural and resistive features with a large hysteresis. The observed anomalies can be explained by a change in the spin state of the cobalt ions, which is extremely sensitive to parameters of the crystal field acting on the ions, as well as by the spin-transition-induced delocalization of electrons.