Who did the disciples of Jesus believe he was?

Answer 1

We do not know what all the disciples believed individually, but according to Mark's Gospel we do know who Peter thought he was and we do know who others thought Jesus was. This is clearly shown in the Gospel's framework structure, which not only shows how passages are often linked sequentially, but also how they are linked in pairs across the entire Gospel:

A . John explains the coming of Jesus (Mark 1:1-8)

B .The baptism of Jesus (1:9)

C . The voice of God from heaven, "Thou art my beloved son" (1:11)

D . The forty days in the wilderness as an allusion to Elijah and Moses (1:13)

E . The people were astonished at what Jesus taught (1:22)

F . Jesus casts out an unclean spirit (1:23-26)

G . Pharisees took counsel with the Herodians how they might destroy Jesus (3:6)

H . Demons, whenever they see Jesus, fall down and say that he is the Son of God.

-- Jesus commands that they tell no one of this (3:11-12)

I .. Jesus calls the 12 disciples (3:13-19)

J .. Jesus rejects his own family: he has a new family, his followers (3:31-35)

K . Jesus rebukes the wind (4:36-41)

L . The demoniac, wearing no clothes (5:15), cries out that Jesus not torment him and Jesus sends out the demons (5:1-20)

M . Jesus comes into his own country (6:1)
-- Where he was brought up

N . The people misunderstand Jesus and he can do no mighty work (6:2-6)

O . Jesus sends out the disciples and curses those who will not receive them (6:7-11)
-- in sending the disciples with authority and expecting all to receive them, Jesus is asserting his own authority

P . Herod thinks that Jesus is John the Baptist risen from the dead (6:14)

Q . Herodias and her daughter conspire to kill John the Baptist (6:16-29)

R . Feeding the thousands, and related miracles and discourses (6:33-8:21)

S . Who do people say that I am (8:27)

T . Peter affirms faith in Jesus as the Christ (8:29)

U . Whosoever shall be ashamed of me: of him also shall the Son of man be ashamed (8:38)

V . The Son of Man must suffer many things and be rejected by the elders, chief priests and scribes (8:31a)

W . Be killed and after three days rise again (8:31b)

X . Prophecy of second coming (9:1)- Jesus tells the disciples that some of them would not taste death until they saw the kingdom of God coming with power.

B' .The Transfiguration of Jesus (9:2-3)

C' .The voice of God from heaven, "This is my beloved son" (9:7)

D' . Jesus talks to Elijah and Moses then to the disciples about Elijah (9:4-13)

E' .A great multitude was amazed at Jesus (9:15)

F' .Jesus cast out a dumb spirit (9:17-27)

G' .They shall kill the Son of man and he shall rise on the third day (9:31)

H' .Jesus clarifies his divine status, saying that he is not God: "Why call me good? There is none good but God" (10:18)

I' . Peter says the disciples have left all and followed Jesus (10:28)

J' . Those who have left their family for Jesus have a new family: all Jesus' followers (10:29-30)

K'. Jesus rebukes the 'sons of thunder', James and John (10:35-45 - cf 3:17)

L' .Blind Bartimaeus cries out for mercy and casts off his clothes, then Jesus heals him (10:46-52)

M' .Jesus comes into Jerusalem (11:1-10)
-- Where he will die

N' .Jesus misunderstands the fig tree that can provide no fruit (11:13-14)

O' .Jesus casts out them that sold and bought in the Temple and curses them for making the Temple a den of thieves (11:15-17)
-- Jesus is asserting his authority

P' .Jesus asks whether the baptism of John is from heaven or of men, and the priests, scribes and elders can not answer (11:30-33)

Q' .Parable of husbandmen who conspire to kill the vineyard owner's son (12:1-9)

X' .Prophecy of second coming (chapter 13)

-- on clouds of glory, within the lifetimes of some of those to whom he was speaking

R' .The Last Supper (14:17-25)

S' .Art thou the Christ, Son of God (14:61)

T' .Peter denies Jesus three times (14:66-72a)

U' .And when he thought thereon, Peter wept (14:72b)

V' .The chief priests, elders and scribes delivered Jesus to Pontius Pilate (15:1)

-- Delivering Jesus is a similar concept to rejecting him.
-- Both parts of the pair involve chief priests, elders and scribes

W' .Jesus dies and on the third day rises again (15:37, 16:6)

A' .The young man explains the departure of Jesus(16:6-8)

In event P, we see that Herod thinks that Jesus is John the Baptist raised from the dead. This creates emphasis for event P', when Jesus asks whether the baptism of John is from heaven or from man, and they can not answer.
In event S, Jesus asks who others say he is, and the disciples say that some say John the Baptist and some say Elijah. Jumping forward to event S', the high priest demands to know if Jesus is the Messiah or the son of God. In event T, Jesus asks who the disciples say he is, and Peter says he is the Messiah. But in event T', he denies Jesus not once, but three times.

On Peter's initial statement, perhaps the disciples thought he was the Messiah, but his later denial shows that not to be a very strong conviction.

Answer 2

Some of them thought he was Elijah. It was only Peter that recognized Him as the Son of God.