The first two stories in La continuación y otras páginas are childhood stories.
The first is "Extraña visita," in which a little girl named Leonor goes with her father to visit her father's friend, who has a daughter her own age. There's some neat descriptions in this short story, such as the friend being "so tall that he seems isolated from the world by his height" and of Elena, the daughter, having black hair but a face "so transparent that it seemed as if it had been erased." While playing, the girls spy on their fathers talking in the study. (Their sight is distorted by a white curtain drawn across the window.) Leonor gets the impression that her father is crying, but afterwards his demeanor convinces her that she must have been mistaken. They don't go back to Elena's house, and Leonor finds that Elena's face has been erased from her memory. Not much happens, so this story is largely about its use of language and imagery, which it admittedly does pretty well.
"La siesta en el cedro" centers on Elena, who may or may not be the same girl from the previous story. Elena is friends with the gardener's daughters, Cecilia and Esther. Cecilia comes down with an illness which has apparently already killed three other people. Elena doesn't really care--she even drinks from a glass that Cecilia has drunk from--but her parents make sure to keep Cecilia away. Cecilia dies, and Elena goes to vist the family but is disgusted as to the extent that they seem to be getting on with their lives.
There's a certain sadness to both stories, stronger in the second, as well as a sense of mystery. The mystery isn't supernatural so much as a product of the interaction between children and adults. In a way, I'm reminded of Julio Cortazar who also wrote short stories about childhood with their fair share of mystery and sadness.