On their way to Pago Pago for a musical stint, Josie and her companions find themselves in troubled waters when the ship on which they are sailing is torpedoed by Captain Nemo, a swarthy scoundrel intent on avenging his great grandfather's name by sinking every ship in the world.
Over the Amazon, the companions become part of a cargo drop on Dr. Greenthumb's supply zone. Greenthumb, a diabolical scientist who schemes to destroy all living flora with his lethal creature plants, brings the group to his plantation where he sends them for a walk along his deadly garden path.
After checking in at the Bombay Tilton Hotel, Alan, Josie and Alexandra are kidnapped by Kaseem, a political usurper who leads a band of hooded scalawags called the Secret Six, and taken to his sanctuary.
A skiing vacation in the Alps accidentally leads the gang to the mountain fortress of Midas, a gold hoarder who has invented a gold-destroying blue microbe mist with which he is seeking to dissolve the world's supply of gold.
The Pussycats befriend Professor Isaac Belfour, a scientist who invented an invented an invisibility formula. They take him along for their gig in Puddletown, England, to protect him from Mr. X, a former laboratory assistant who stole the formula.
The Pussycats are involved in an atomic chase in Mexico when they are pursued by The Scorpion, a power-hungry ringleader who is after a vial of glowing nuclear capsules hidden in the hollow of Melody's drum.
The Pussycats are doomed for stardom when the dirigible in which they are performing at the World Expo in Florida takes off and lands on the island of Dr. Strangemoon, a diabolical scientist who plans to launch satellites that will attract comets and cause world-wide disasters.
The Pussycats accidentally get their paws on a top secret blueprint intended for the World Scientific Foundation and are returning the material to the Foundation when intercepted by The Lazer. He is a maniacal wizard who schemes to build a device from the blueprint capable of stopping all the machinery in the world.