More than 60% of trains are failing to arrive on time in Arbroath and Carnoustie.
North East region Scottish Conservative MSP Bill Bowman said things keep getting worse.
The percentage of trains stopping on time in Arbroath was, on average, 39.7% in the four months from November to March. The figure for Carnoustie over the same period was 39.0%..
Mr Bowman said: “The issue of trains stopping at Arbroath on time is raised frequently, but it keeps on getting worse.
“More than 60% of trains arrive late, and Carnoustie is faltering at 61% over the last three months. Arbroath commuters often complain of stop-skipping, where late-running services barrel through to get to Aberdeen.
“More than a year ago, the SNP transport minister pledged to put an improvement plan in place. No improvement has been forthcoming.
“I urge ScotRail and Transport Scotland to buck up the service, without resorting to stop skipping.”
Angus South SNP MSP Graeme Dey said he did secure undertakings from ScotRail around the practice of stop skipping and train capacity for major sporting events, both of which he raised directly with the companies CEO Alex Hines.
He said: “Missing stops is acceptable only in exceptional circumstances and ScotRail acknowledged this.
“They are working to reduce the scale of such occurrences in Angus and elsewhere.
“As regards sufficient capacity for the likes of rugby and football internationals, the upcoming 25% increase in available rolling stock provides an opportunity to ensure trains journeying through Angus to the likes of Glasgow and Edinburgh are of a length that travellers can secure seats.
“I am well aware of the uncomfortable journeys that some of my constituents have endured recently travelling to and from rugby matches at Murrayfield.”
The firm has clocked up £3million in financial penalties over the first nine months of this financial year for its failings, having posted a £3.5m after-tax loss for 2016.
That is double the financial penalties imposed on them for the whole of the previous year.
A ScotRail Alliance spokesperson said: “We know how frustrating delays, cancellations and skip-stopping can be for customers.
“Skip-stopping is something that we only do when absolutely necessary, to prevent further disruption across the network.
“We are very clear that it should always be a last resort.
“Despite recent challenges, ScotRail remains the best performing large operator in the UK. But we want to deliver even more for our customers, and because we rightly expect the highest standards, we are implementing a number of initiatives to improve both the reliability of our trains and the supporting infrastructure.
“We are investing hundreds of millions of pounds improving Scotland’s railway.
“The work we are doing will mean faster journeys, more seats and better services for our customers.”