Great Britain's Jess Varnish and Becky James won bronze as the men's sprint and pursuit teams endured a tough first day at the Track Cycling World Championships in Cali, Colombia.
Varnish and James were third in the women's team sprint but the two men's squads failed to reach their respective medal ride-offs.
The sprint team were fifth, while the pursuit quartet finished eighth.
"We've had some problems," said pursuit rider Ed Clancy.
Britain won the four-man pursuit event in 2012 and took silver in 2013. They also won gold at the 2008 and 2012 Olympic Games.
But two-time Olympic gold medallist Clancy, Sam Harrison, Owain Doull and Jon Dibben finished eighth this time in four minutes 4.419 seconds as Australia won the 4km event ahead of Denmark.
It was Britain's worst performance for 15 years, although London 2012 gold medallist Steven Burke was missing from the line-up after failing to recover from illness.
"We knew a week ago our back was against the wall," added Clancy. "Despite the fact we didn't have a couple of our more established riders in the line-up, we were still hoping to get a ride in the final."
London 2012 champions Phil Hindes and Jason Kenny combined with Kian Emadi to come fifth in the sprint event over three laps.
Britain have not won the world title since 2005 - when Sir Chris Hoy, in Cali for this event as a team mentor, was part of the squad - and have now missed out on a medal for a third successive year.
Kenny has never worn the world champion's rainbow jersey in the team sprint and Britain's wait for a world title will extend to 10 years.
Kenny, who will bid to defend his keirin title on day two, said after his 43.617 secs ride: "It is frustrating for me. I've got a lot of medals in this event over the years, not many of them gold. We've got the Olympic gold medals, which is the main one.
"We're disappointed with the result, but the time itself and the way we rode wasn't that bad."
New Zealand qualified fastest and Ethan Mitchell, Sam Webster and Ed Dawkins won the final in 42.840 secs ahead of Germany (42.885).
In the women's team sprint event, Varnish and James won the ride-off for bronze ahead of Russia, clocking 33.032 secs.
"It was a solid performance," Varnish said. "It's a really different track to what we've ridden on and you can't really compare it to other performances. I think we should be happy."
Germany's Miriam Welte and Kristina Vogel, the Olympic champions and world-record holders, won a third straight world title in 32.440 secs, with China second.
The World Championships are taking place at a track exposed to the elements, with a roof but without walls, but the forecast rain did not arrive and so proceedings were not disrupted.
Thursday will see medals decided in the women's team pursuit and 500m time-trial, along with the men's keirin, individual pursuit and scratch race.