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Summary

  1. Griffiths (2, 1 pen), Ralston, Tierney & Armstrong score as Celtic beat Killie
  2. Stokes (2), Murray, Ambrose & Matulevicius on target as Hibs defeat Ayr
  3. Lawless (pen), Edwards & Erskine net as Partick Thistle win away to St Johnstone
  4. Livingston beat Falkirk after extra time, De Vita & Robinson for Livi, Craigen for Falkirk

Live Reporting

By Andy Campbell

All times stated are UK

  1. Hopkin joy as Livi reach last eight

    FT: Falkirk 1-2 Livingston

    Livingston manager David Hopkin: "Our fitness levels are incredible.

    "When it went to extra-time, I had no qualms we were going to win the game.

    "We've scored two fantastic goals and I think we're unlucky not to score a few more.

    "To progress again, it's great credit to my staff and my players."

  2. Four through, four ties to go

    I'm going to call it a night.

    Thank you for joining us for Tuesday's Scottish League Cup coverage and come back tomorrow for Wednesday's ties with more radio and text updates.

  3. Wednesday's ties

    Scottish League Cup second round

    • Dundee v Dundee United
    • Hamilton Academical v Aberdeen
    • Rangers v Dunfermline Athletic
    • Ross County v Motherwell
  4. Jags boss savours Perth win

    FT: St Johnstone 0-3 Partick Thistle

    Partick Thistle manager Alan Archibald: "Absolutely delighted.

    "Loads of energy in the second half. We really drove the game home.

    "Hopefully, we can kick on in the league now. We've got another tough one next with Celtic but thankfully we're in the next round."

  5. FULL-TIME

    Falkirk 1-2 Livingston (aet)

    It's all over at the Falkirk Stadium and it's Livingston who go through to the Scottish League Cup quarter-finals, getting the win in extra time.

  6. PENALTY APPEAL

    Falkirk 1-2 Livingston

    Dylan Mackin hits the deck inside the box but the referee waves play on. It's Livingston who are doing all the pressing as time ticks away for the home side.

  7. GREAT SAVE!

    Falkirk 1-2 Livingston

    Robbie Thomson makes a terrific save to deny Josh Mullin and keep Falkirk in the tie.

  8. Lennon delighted with 'fantastic' Hibs

    FT: Hibernian 5-0 Ayr United

    Hibernian head coach Neil Lennon: "They showed the right attitude and had real good quality about them as well.

    "[Anthony Stokes] was fantastic - far better than I expected. When you consider that that's his first 90 minutes in over a year, I've got to be delighted with his contribution.

    "Going forward we look pretty strong at the moment."

  9. EXTRA TIME

    Falkirk 1-2 Livingston

    The second period of extra time is under way at the Falkirk Stadium with Livingston still narrowly ahead.

  10. Rodgers pleased with 'brilliant' Celtic

    FT: Celtic 5-0 Kilmarnock

    Celtic manager Brendan Rodgers: "It was a brilliant team performance.

    "They showed real good tempo and speed in their game.

    "A lot of young players playing this evening. It shows you that it's not just about the high profile guys.

    "[Kieran Tierney] has got a wonderful strike on him. The power that he's got in it was phenomenal. He's a talent that's only going to get better."

    Brendan Rodgers
  11. HALF-TIME in EXTRA TIME

    Falkirk 1-2 Livingston

    Livingston have the advantage but must negotiate another 15 minutes at the Falkirk Stadium if they are to join Celtic, Hibernian and Partick Thistle in the quarter-finals.

  12. GOAL Falkirk 1-2 Livingston

    Raffaele de Vita

    Raffaele de Vita scores his first goal of the season from Josh Mullin's cross and Livingston are back into the lead.

  13. Quarter-finals next month

    The four winners from tonight and the four from tomorrow's ties will find out their quarter-final opponents when the draw is made shortly after Wednesday's ties.

    Those last-eight matches will be played on 19, 20 and 21 September.

  14. EXTRA TIME

    Falkirk 1-1 Livingston

    Still no further scoring at the Falkirk Stadium and neither goalkeeper has been seriously tested so far in extra-time.

  15. Celtic's cup defence begins in style

    FT: Celtic 5-0 Kilmarnock

    Kenny Crawford

    BBC Sport Scotland at Celtic Park

    "What a statement that is from Celtic, who with a largely second-string starting XI showed they still have the quality to give established top-flight clubs like Kilmarnock a torrid time.

    "The highlight of the night looked like it would be Anthony Ralston's first senior goal, but that was eclipsed when captain Kieran Tierney despatched a brilliant long-range strike into the top right corner.

    "Leigh Griffiths notched a brace and Stuart Armstrong rounded off the scoring, with the likes of Scott Sinclair and Callum McGregor on the bench not even required."

    Celtic celebrate
  16. FULL-TIME

    St Johnstone 0-3 Partick Thistle

    Three second-half goals send Partick Thistle through to the last eight as Premiership rivals St Johnstone bow out of the League Cup.

    Steven Lawless scores a penalty
    Image caption: Steven Lawless' penalty set Partick Thistle on their way to victory
  17. FULL-TIME

    Celtic 5-0 Kilmarnock

    Celtic comfortably through to the quarter-finals and the holders will take some stopping in this season's League Cup.

    Kieran Tierney scores
    Image caption: Kieran Tierney scored from long range as Celtic routed Kilmarnock
  18. EXTRA TIME

    Falkirk 1-1 Livingston

    No winner in regulation time so the tie at the Falkirk Stadium is heading for extra time.

  19. GOAL St Johnstone 0-3 Partick Thistle

    Chris Erskine

    That should be that in Perth as Chris Erskine evades a couple of defenders to fire in Partick Thistle's third.

  20. FULL-TIME

    Hibernian 5-0 Ayr United

    Hibernian safely and comfortably through to the Scottish League Cup quarter-finals with a big win over Ayr United.

    Efe Ambrose scores
    Image caption: Efe Ambrose was one of Hibs' scorers