Applications for the grants are now being invited by ELWa - the Welsh lifelong-learning quango - while, in England, the creation of the long-awaited "ILA Mark 2" has been cancelled by the Department for Education and Skills.
The DfES says its skills White Paper covers many of the objectives of ILAs and there is no longer a need for a self-standing scheme.
The Welsh scheme was suspended after the English ILAs were dropped in November 2001, amid allegations of abuse and fraud.
But the suspension of the Welsh scheme, the following month, had been purely precautionary - with the national assembly reporting that it had not suffered from the security problems which plagued the English scheme.
Unlike the English scheme, run by private contractor Capita, it was not administered by a private-sector partner.
As before, Welsh ILAs will be run by ELWa on behalf of the assembly, with a pound;2 million budget for its first year.
The new version is aimed at people who are not qualified beyond level 2 (GCSE grade C equivalent). Subsidies range from pound;200-a-year for those on income support to pound;100 for people in work but on low incomes.
ELWa has compiled a list of 115 approved "providers" - including further education colleges and private companies - whose courses will qualify for the subsidies.
Joan Lockett, ELWa's ILA manager, said: "There was no evidence of abuse in Wales but, because of the history of ILAs in other parts of Britain, we have been extremely rigorous in the way we have set up the new scheme.
"This time, we are delivering the programme through a smaller, tighter network of learning providers who have been carefully chosen against strict criteria."
While the new ILAs will not be available to better-qualified adults, as was the case under the original scheme, the new version will allow both accredited and non-accredited courses to be subsidised. The principle, as before, is to get adults into the habit of learning.