Kent 482 for 8 dec (Stevens 237, Billings 138, Olivier 5-108) and 2 for 0 lead Yorkshire 268 (Fisher 47*, Milnes 5-87) by 215 runs
Kent have strengthened their grip on their penultimate-round Specsavers County Championship clash with Yorkshire at Headingley.
Both counties may be out of the title running in Division One, but they are in a three-way battle for third place in the table alongside Hampshire, with Yorkshire currently holding that position.
Kent declared their first innings on 482 for 8 immediately before the start of day two before chipping away at the wickets on an excellent batting surface, with the hosts bowled out for 269 shortly before close. Kent, with a lead of 213, opted not to enforce the follow-on and reached close at two without loss from two overs in their second innings.
Day-one double centurion Darren Stevens claimed two Yorkshire wickets and Matt Milnes 5 for 87 from 21 overs, although some of the gloss from Kent's day was taken off by six dropped catches.
Early on each day has been the best time to bowl, with Kent 39 for 5 on day one before recovering and Yorkshire 36 for 3 - Matt Fisher top-scored for them with a career-best 47 not out.
Stevens did the initial damage to back up his sensational career-best 237. He struck twice in five balls in the eighth over, getting Adam Lyth caught low down at second slip by Faf du Plessis before trapping Gary Ballance lbw the ball after he had been dropped at third slip by Zak Crawley.
That left Yorkshire at 17 for 2 before teenage debutant Matty Revis, dropped on nought and eight, edged Milnes' fourth ball behind in the 18th over for nine. Lyth and Ballance had also fallen for single-figure scores.
Kent's six dropped catches were all in the morning and afternoon, with wicketkeeper Ollie Robinson and slip fielders Crawley and Ollie Rayner all letting two chances go by.
While day one was helter-skelter, day two was hard-fought, with both sides working for reward.
Either side of lunch, Tom Kohler-Cadmore and Harry Brook, who made 36 apiece, shared 59 for the fourth wicket before falling inside five early afternoon overs as the hosts fell from 95 for 3 in the 33rd over to 106 for five after 37. Both men fell to Milnes, with Brook first to go lbw to one which kept low. Kohler-Cadmore then lost his off stump as he tried to leave alone.
Kent struck again in the 47th over, this time through Stevens' new-ball partner Harry Podmore, who had Jonny Tattersall caught at third slip by Crawley as the score fell to 141 for 6.
But batting recovery has been a theme of this fixture, and seventh-wicket pair Tim Bresnan and Fisher continued the trend either side of tea to take their side to the cusp of 200 and a first batting bonus point. They calmly chalked up a half-century stand inside the opening 10 minutes of the evening session, only for it to end on 53 when Milnes uprooted Bresnan's off stump for 39.
Podmore struck again in the first over with the new ball as he bowled Steve Patterson, leaving the score at 220 for eight. Milnes then claimed his fifth when Duanne Olivier was trapped lbw. By this time, Fisher had topped his previous best score of 37, and Ajaz Patel edged a boundary to secure a second batting point. Patel was bowled for 20 sweeping at Rayner's off-spin to wrap up the Yorkshire innings.