text: Carmarthenshire's Mark James and Pembrokeshire's Bryn Parry Jones had been given cash payments in lieu of employer pension contributions.
  Dyfed-Powys Police said the force was in discussions with the auditors.
  Carmarthenshire council said it was pleased the auditor did not rule its pension policy as unlawful.
  The public spending watchdog report said that both authorities had acted unlawfully in allowing the chief executives to opt out of the Local Government Pension Scheme (LGPS) to avoid potential tax payments.
  Mr James was also unlawfully given an indemnity against potential libel costs.
  Assistant auditor general Anthony Barrett said: "Carmarthenshire council has acted unlawfully on two fundamental issues, both of which the public need to be fully aware of.
  "The authority has taken decisions and used taxpayers' money in areas that they do not have the legal powers to do so."
  In a separate report on Pembrokeshire council, Mr Barrett concluded similar pension arrangements for some senior officers were also contrary to law.
  It is expected that by the end of March 2014, £51,011 will have been paid to chief executive Mr Jones and one other senior officer.
  The auditor said the decisions to allow certain officers to receive payments, and then for payments to be made, were unlawful on several grounds.
  "The public should be able to expect the highest standards of decision making at local authorities and the council must now address the procedural weaknesses I have identified in my report," he said.
  "It needs to demonstrate to its electorate that it is operating in accordance with the law and in line with good governance principles."
  Mr Barrett said neither council had the lawful power to give cash supplements in lieu of pension contributions to avoid tax liabilities, but said it was up to the local authorities whether they tried to claw back any money.
  Mr Barrett conducted two reports into Carmarthenshire council - the first into pension payments, and another into the decision to grant an indemnity to the chief executive to bring a libel counterclaim.
  He said the council acted "contrary to law" by allowing senior officers to opt out of the LGPS.
  More than £27,000 was paid to Mr James under the scheme since 2012.
  Mr Barrett said the council had since "rescinded its decision to offer a pay supplement in lieu of pension contributions and announced that no further payments will be made to the chief executive from January 2014".
  The original decision taken in November 2011 was considered by the council's executive board without appearing on the agenda and without being open to inspection by members of the public.
  In his report on the libel indemnity, the auditor said the council "does not have the legal powers to make such payments and there were inadequacies in the processes adopted by the council when making the decision".
  It concerned Mr James's libel action against Jacqui Thompson, a blogger who was arrested after filming a council meeting on her mobile phone.
  He won the case and Ms Thompson was ordered to pay costs of £23,217.
  Her own attempt to sue Mr James for libel during the course of the dispute was rejected.
  Carmarthenshire has paid out more than £26,000 in external legal costs since 2012 under the decision to indemnify its chief executive.
  The auditor added: "The libel counterclaim is still on-going and it is unclear what the final external legal costs to the council will be."
  Carmarthenshire council said is was pleased the report did not think its pensions policy was unlawful but that its procedural process was flawed.
  It said steps had been taken to sure ensure such matters are considered as separate items on an agenda.
  The council said it remained convinced that indemnifying Mr James in the libel action was correct, and claimed the audit office had not objected to the policy when first consulted on it.
  The local authority noted that the audit office had changed its mind on the issue some months later, and claimed it was "too late for us to turn back the clock".
  Pembrokeshire council also insisted its pension payment policy was lawful.
  Reacting to the report, deputy leader Rob Lewis said: "While I note the auditor's views in relation to the decision taken, I am pleased he has concluded the council could take a lawful decision once a number of procedural matters have been addressed."
  Janet Finch-Saunders, the Welsh Conservatives' shadow minister for local government, said: "These reports are further evidence of the need for a Wales-wide review of senior pay in Welsh local authorities, which is out of control and failing to deliver value for money for hardworking families."
  She told BBC Good Morning Wales: "We do have some excellent local authorities, but this has cast a shadow now over... our chief executives, who do work within their remit in an honest and transparent manner.
  "As to the consequences, it's time now for the chief executive Mark James to resign or, certainly, be instantly dismissed."
  Meanwhile, Plaid Cymru called for councillors who approved Carmarthenshire's pension and libel case payments to resign.
  Rhodri Glyn Thomas, the party's AM for Carmarthenshire East and Dinefwr, has also called for Mr James to quit.
  He added: "This is a very dark day for Carmarthenshire, a dark day for democracy in Carmarthenshire, and is an example of what happens when you have a very weak executive and a council controlled by powerful unelected officers."
  The chair of the public accounts committee, Darren Millar, said the reports showed both councils had fallen well below expected standards.
  The committee will now consider these findings as part of a wider inquiry into senior managers' pay in the Welsh public sector.
  Dyfed-Powys Police said it was "aware of the reports" and "whilst the matter hasn't been referred to us, we are in discussions with the auditor and will be making an assessment in relation to any appropriate action by the police".
target: Two councils acted unlawfully by letting chief executives opt out of a pension scheme to avoid potential tax payments, the Wales Audit Office says.