Kantar said Bradford-based Morrisons saw sales decline 1.7 per cent while Leeds-based Asda's sales fell 1.2 per cent in the 12 weeks to November 3.
Fraser McKevitt, head of retail and consumer insight at Kantar, said it was hard to pin down why Morrisons and Asda are both underperforming.
"They've been towards the bottom of the pack for the last couple of months and they've been caught by the general market slowdown," he said.
"It was a little bit unexpected if I'm honest. You would have expected growth to pick up this month as we've stopped annualising against last year's really bumper summer.
"You might have expected growth to accelerate rather than go backwards so I think it's a combination of confidence is not particularly high, there's political uncertainty and the economy is not feeling particularly great, despite the economy avoiding recession."
He said a combination of all of these things is leading to a general slow performance at the big four and Asda and Morrisons are included in that.
"Both Asda and Morrisons have seen a slight reduction in the number of shoppers coming through their door compared with last year," he added.
However, he said there were a couple of "bright spots" for the Yorkshire duo.
"Asda's confectionery sales were up 8 per cent in October for Halloween," he said.
"The most noticeable thing about Morrisons is they still have the highest level of promotion in the market compared with their rivals, but it doesn't seem to be getting more people through the door at the moment."
A Morrisons spokesperson said: "We don't recognise Kantar's research or commentary on our level of promotions."
Analyst Bruno Monteyne at Bernstein said: "Morrisons' first half results were decent and the commentary going into the second half was positive.
"However, the recent trend of being the worst performer out of the big four, compared to before the turn of the year when it was the bestperformer, has become more and more noticeable."
He said this run of "poor data" is starting to become "worrying for the smallest of the big four".
He added: "Asda was second-worst versus its peers. This is a rough continuation of trend for Asda as the second worst performer in the big four."
All of the big four supermarkets saw a slow start to the crucial festive period.
Sainsbury's and Tesco proved slightly more resilient than their Yorkshire rivals with falls of 0.2 per cent and 0.6 per cent over the 12 weekperiod.
Lidl was the fastest growing bricks and mortar retailer with sales up 8.8 per cent. Unlike the big four players, Aldi and Lidl continue to open lots of new stores.
Year-on-year supermarket sales overall grew by 1 per cent, down slightly on last month, against a backdrop of political uncertainty and a persistently wet autumn, as retailers turned their attention from Halloween to Christmas.
Mr McKevitt said: "This year pumpkin sales were up by 6 per cent in October as the public geared up for Halloween - with more than a tenth of British households taking one home. In the past decade pumpkin sales have increased by 62 per cent - a telling barometer of how retailers have found success by increasing focus on seasonal spend.
"With many supermarkets already unveiling their festive advertising campaigns, the starting gun has been fired on the race to be Christmas number one. It should come as no surprise to see the grocers jostling for position early - with the average household expected to spend more than £380 on groceries during December. In total, shoppers will spend nearly £11bn in that month alone, showing how it's a crucial period for retailers."
Figures from analysts Nielsen also showed consumers holding back on grocery spend at the top four supermarkets as sales rose by just 1.1 per cent in the last four weeks.
Mike Watkins, Nielsen's UK head of retailer and business insight, said: "The in store promotional activity ahead of the festive period, from Halloween to retailers' money-off vouchers, clearly proved less effective with consumers as grocery sales largely fell flat in the last four weeks at the big four supermarkets.
"Whilst the economy remains Brits' number one concern, rising food prices and global warming are climbing up the agenda, and are all motivating shoppers to spend differently. Moreover, with the continued uncertainty around Brexit and now a General Election on the horizon, shoppers are increasingly adopting a savings mindset."