Aims. Search for Very High Energy γ-ray emission in the Kookaburra complex through observations with the HESS array.
Methods: Stereoscopic imaging of Cherenkov light emission of the γ-ray showers in the atmosphere is used for the reconstruction and selection of the events to search for γ-ray signals. Their spectrum is derived by a forward-folding maximum likelihood fit.
Results: Two extended γ-ray sources with an angular (68%) radius of 3.3-3.4′ are discovered at high (>13σ) statistical significance: HESS J1420-607 and HESS J1418-609. They exhibit a flux above 1 TeV of (2.97 ± 0.18stat ± 0.60sys) × 10-12 and (2.17 ± 0.17stat ± 0.43sys) × 10-12 cm-2 s-1, respectively, and similar hard photon indices ~2.2. Multi-wavelength comparisons show spatial coincidence with the wings of the Kookaburra. Two pulsar wind nebulae candidates, K3/PSR J1420-6048 and the Rabbit, lie on the edge of the HESS sources.
Conclusions: The two new sources confirm the non-thermal nature of at least parts of the two radio wings which overlap with the γ-ray emission and establish their connection with the two X-ray pulsar wind nebulae candidates. Given the large point spread function of EGRET, the unidentified source(s) 3EG J1420-6038/GeV J1417-6100 could possibly be related to either or both HESS sources. The most likely explanation for the Very High Energy γ-rays discovered by HESS is inverse Compton emission of accelerated electrons on the Cosmic Microwave Background near the two candidate pulsar wind nebulæ, K3/PSR J1420-6048 and the Rabbit. Two scenarios which could lead to the observed large (~10 pc) offset-nebula type morphologies are briefly discussed.

