“You killed me, Kuryakin. Why?”
Still not sure whether he was dreaming this encounter or not, Illya decided the best option was simply to play along. Maybe his ghost would go away sooner that way. “It had to be done,” he said flatly.
“Did it now.” The spirit resumed his circling of the bed. “You and Solo already had me caught. U.N.C.L.E.’s usual method is a sleeping dart in the back of the neck. But you went right for the kill.” At the foot of the bed, he started to untie the cloth belt around his trenchcoat.
Illya tensed slightly. “I prefer to make sure my enemies can’t come back to haunt me,” he said, his tone and choice of words deliberately dry and ironic.
---The Mist of Yesterday
Ah, Illya and Mr. Ecks. Aside from Ecks and Wye's interaction, this is probably what I have the most fun with. Ecks is such a cheeky sort who loves to pester Illya when they encounter each other. Illya responds with his usual calm, cool, and aloof demeanor. But they can end up having deep conversations, as in The Mist of Yesterday.
Ecks and Illya don't exchange so much as one word in canon, but Illya cements their ties when he twists the captured Ecks' hand around and stabs him with his own knife in Hyde Park.
When Ecks was recovering from being wounded, he was very ill and repeatedly and unwillingly left his body. Somehow he learned who Illya was and where he was during one of those exploits and started visiting him during those out of body experiences. Each believed the initial encounter to be a dream later on, although Illya quickly realized he was being haunted instead. Ecks did not remember and realize what had happened until much later. Perhaps he knew deep down, but didn't want to accept it. He had a difficult time accepting that such a thing happened to him and preferred to continue believing it was just a strange series of dreams.
Ecks persisted in his stalking of Illya after his recovery, albeit not to seek revenge or even just to be cheeky, but simply to prove to himself that he still had what it takes to be a good spy. Once he had had enough of his game, he revealed himself to Illya and left him alone. Illya, although aggravated at having been stalked, showed no outward surprise that Ecks was alive. They shared a sassy but serious conversation before parting ways.
Subsequent encounters are generally unwelcome and filled with sassy and sarcastic remarks. When they discover they are each working on The Peaceful Meadows Affair, their initial reaction is to attempt to out-spy each other. Following an accidental collision, they each place a listening device on the other. Ecks is at his most cheeky when he discovers his; his prompt reaction is to drop it in a garbage can, in full view of Napoleon and Illya. After Illya discovers his while retrieving the wayward bug, he deposits his in the same garbage can. Napoleon objects to the immature nonsense, but it takes a while before all four spies can agree to a truce. Even then, Ecks and Illya are hesitant about shaking hands.
While they do not particularly like each other, they do respect each other's talents and will even help each other if the situation calls for it. Illya goes as far as to save Ecks' life when Ecks is killed rescuing Napoleon during a vicious blaster gun battle.
They are teamed again during the search for the rogue Ms. Cue and share a great deal of snark and sarcasm. They are also both experiencing dream-memories of their encounters when Ecks continually wandered out of his body, though neither wishes to admit it to the other.
Though Illya would never admit it to Ecks, he told Napoleon once that in some ways, he sees Ecks as a dark mirror of himself. Napoleon mused that had their situations been different, perhaps he and Illya would have worked for the extremist organization while Ecks and Wye would have been U.N.C.L.E. agents.