Okay; finally, it works.

Here is my code I had to correct according to Sougata's example.

Code:
' Fuses
@ DEVICE PIC16F88,INTRC_OSC_NOCLKOUT
@ DEVICE PIC16F88,PROTECT_OFF
@ DEVICE PIC16F88,WDT_OFF
@ DEVICE PIC16F88,PWRT_ON
@ DEVICE PIC16F88,MCLR_ON
@ DEVICE PIC16F88,BOD_OFF
@ DEVICE PIC16F88,LVP_OFF
@ DEVICE PIC16F88,CPD_OFF
@ DEVICE PIC16F88,DEBUG_OFF
@ DEVICE PIC16F88,CCPMX_OFF

'-------------------------------------------------------------------------------
' Registers   76543210
OSCCON     = %01100000  '4MHz
OPTION_REG = %10000000  'D I S A B L E PORTB's Pull-Ups for buttons
'ANSEL      = %00000000  'Disable Analogue Inputs
TRISA      = %00000000  'Inputs/Outputs
TRISB      = %00100000  'Inputs/Outputs

'-------------------------------------------------------------------------------
' Variables
Led0  var PORTA.0
Led1  var PORTA.1
HiLow var PORTB.5   'this port is TTL only
InOut var TRISB.5
Time  var byte
time  = 2

'-------------------------------------------------------------------------------
' Program
MAIN:
    inout = 0
    hilow = 0
    pause time
    inout = 1
    pause time
    if hilow = 1 then led1 = 1 : goto main
    led1  = 0
    inout = 0
    hilow = 1
    pause time
    inout = 1
    if hilow = 0 then led0 = 1 : goto main
    led0 = 0
    Goto MAIN
    end
ANSEL or not, it works.

I changed the 0,1µF cap for a 0,01µF and reduced the pause time to 2 so it goes drastically faster.

Thanks a lot for your patience.

In fact, I was stuck in my mind thinking this problem would have to be resolved another way than by a software routine...