Replace your one drawn image:

Thank you for the quick reply.

When adding this code I get the following error:
The method get (int,int,int,int) in the type PImage is not applicable for the argument (int,float,int,float).

image(d.get(0,int(y),d.width,d.height-int(y)),0,0);

Okay, adding that code results in 2 backgrounds laying on top of eachother, 1 going up and 1 going down.

Sorry, I'm really new to processing so I don't immediately know how to look for possible fixes.

Ah! My bad. Try this:

I'll post the entire code for clarity. It's far from done yet.
The objective is to avoid the flames the dragon shoots at you. Both the player and the dragon are bound to mouse x, forcing you to move away. The speed and amount of fire increases over time. I currently only have a moving background and the loaded images.

import gifAnimation.*;

int variabele1;
int variabele2;

float bgrepeat;
float y = 1;
float x;
float speed = 1;


void setup() {
  size(400,600);
  frameRate(25);
  smooth();
  oscP5 = new OscP5(this,"239.0.0.1",7777);
}

void draw() {
  rectMode(CENTER);
  noStroke();
   //uncomment dit voor te testen. variabele1 en 2 hangen dan aan de muiscoordinaten vast
  //als de server draait, comment je deze terug.
  variabele1 = mouseX;
  variabele2 = mouseY;
 
  y = y + speed;//scrollspeed
   
  PImage a; // image object
  a = loadImage("back.png"); //laadt background in als image
  image(a,0,int(y));; //scrollt bg naar beneden
   if(y > height){
       x = bgrepeat;
       y = 0;}
  image(a.get(0,int(y),a.width,a.height-int(y)),0,0);
   
 
  PImage b; // image object
  b = loadImage("player.png"); //laadt player.png in als image
  image(b,variabele1,500); //positie player
 
  PImage c; // image object
  c = loadImage("enemy.png"); //laadt enemy.png in als image
  image(c,variabele1,2); //positie enemy
 
  rectMode(CENTER);
  PImage d;
  d = loadImage("bullet.gif");
  image(d, variabele1+35,90);

 
 //if(y > 0 && x > mouse x + 92 && x < mouse x + 20){
 //} //collision: als y groter is dan bovenkant scherm en x in player is dan collision
}

Okay your code works, thanks!

Now to understanding why it works haha.

I made a few other changes to your code as well:

1) Remove calls to framerate(). This is not the way to do things. If you need to only update variables at a certain frequency, ask about that. It involves calls to millis() and remembering the last time something happened.

2) DO NOT CALL loadImage() IN DRAW()! EVER! HERE ARE A BUNCH OF EXCLAMATION POINTS TO REALLY DRIVE HOME THAT THIS IS WRONG:!!!!!!!!!!!!!!!!!!!! This is loading the background image from memory 60 times A SECOND! You should have a different PImage variable for each of the images you use, and you should loadImage() each one only once, in setup()!

3) Calls to rectMode() and noStroke() can also be moved to inside setup() if you don't want the settings to change at all.

Thanks for the tips. The framerate has been added by my teacher, I myself am not familiar with it. The variables will be controlled on his iphone by commenting the variable code for mouse positions, the framerate was included with a oscp5 library needed for this to work.