Resources in some Cardiff schools are "fit to burst" as the numbers with English as an additional language have risen by up to 400 per cent and a quarter of the school population now have an EAL label.
Elsewhere, service providers also say they do not have the funding they need. Swansea and Wrexham have had to employ extra Polish support staff and one Wrexham secondary with high numbers of Polish pupils is offering a GCSE in the language for the second year running.
The influx is partly due to a rise in the number of migrant workers from new EU countries, particularly Poland. But there are concerns that staff are not properly trained. Graham Edwards, head of education inclusion at Wrexham council, said: "We've had 64 new arrivals already this September and more than half of them are from Poland. In some primary schools more than a third are children from migrant worker families. We would like more funding."
Figures out in England last week from the Department for Children, Schools and Families show that more than one in 10 children in state schools do not speak English as their first language, making it a UK-wide problem.
Critics there say numbers have been underestimated and teaching staff are under increasing strain to help the children become fluent.
The Assembly government will provide pound;8.1 million under the Minority Ethnic Achievement Grant to help local authorities fund services this year, an increase of 9 per cent on 2006-7. But staff working in EAL services will not feel any impact as funding is based on assessments of pupil needs carried out in autumn 2006, not currently. The services are also being hit by local authority budget cuts, say some schools.
Tracey Pead, deputy services leader of Gwent's ethnic-minority support service, said: "Money is tied to the numbers of pupils but the assessment is made once a year and we get new pupils in throughout the year. Retrospective funding is not helpful."
Graham Edwards of Wrexham said: "The funding from the Assembly is very welcome but it's hardly keeping pace with the number of new arrivals.
"At the moment seven or eight primary schools and two secondaries in Wrexham have the bulk of EAL pupils because new families tend to rent in the town centre."
Swansea's ethnic-minority language and achievement service also provides a service for schools in Neath Port Talbot. It says teachers have demanded extra training.
100 Polish-speaking pupils in Swansea and Neath Port Talbot, up from just a handful two years ago.
500 pupils in Cardiff last year who started school with little or no English.
2,960 pupils in Cardiff this year who started school with little or no English a 400 per cent rise.
120 Polish-speaking pupils in Cardiff now. Two years ago there were none.
75 staff employed by the ethnic-minority language and achievement service in Swansea, dealing with SylhetiBengali, Cantonese, Arabic, Tegalog, Polish, Punjabi, Turkish, Urdu and Farsi.