Expositor's Bible Commentary Commentary Mark 1:34

"And he healed many that were sick with divers diseases, and cast out many demons; and he suffered not the demons to speak, because they knew him." — Mark 1:34 (ASV)

The following day (since Sabbath ends at sundown), people could now bring, without breaking the law, their sick and demon-possessed to him. The exorcism of v.26 and the healing of v.31 were not isolated cases. Jesus extended his healing power to large numbers.

Again Jesus muzzled the demons, “because they knew who he was” (cf. Lk 4:46). His reluctance to have the demons reveal him as the Messiah is best explained by his desire to show by word and deed what kind of Messiah he was before he openly declared himself as the Messiah.