Mr Hughes and Mr Shaw both gave a nod to outgoing Greens co-leader Russel Norman in their five minute-speeches today.
Wellington-based Mr Hughes said he wanted to take the party over the 15 per cent mark, and if elected, would make Auckland a priority, which would mean moving with his family to live in New Zealand's biggest city.
"I believe a co-leader should live here full-time," he said.
The party's female co-leader Ms Turei is Dunedin-based, while Mr Norman lives in Wellington.
Mr Shaw said the Greens co-leader needed to have economic credibility and named climate change as his number one priority.
He said the party must continue its growth and transformation into a body with a broad base, otherwise New Zealand's next government would be decided by Winston Peters.
Mr Hague - who is Greens spokesman for ACC, health, and housing - among others, said he wanted to take the party into Parliament with the strength to deliver transformative economic and environmental changes.
"I am hungry for the opportunity to represent the Green Party's values."
As the only non-MP hopeful to run for co-leadership, Mr Tava said it was important the party identified with neither the left nor right.
He said issues of environment and social responsibility were not only for the left wing, and both needed to be considered to create an "integrated solution" to global warming.
Green members will vote at the party's AGM on May 30, after which Mr Norman's replacement will be announced.
Ms Turei is the sole nomination for female co-leader, so will be re-elected.