I now upgrade my ubuntu version, removed afni and reinstalled the newest afni version from this page. I then ran into a different error, namely:

3dvolreg.afni: error while loading shared libraries: libmri.so: cannot open shared object file: No such file or directory
ERROR: 3dvolreg.afni
Invalid null command.

I fixed this error by downloading again the NeuroDebian afni version and copying the libmri.so file to the new afni verison. Then I removed the NeuroDebian afni again. Unfortunately my original error remains though. Here the current error message and my afni system_check output:

Fatal Signal 11 (SIGSEGV) received
mri_add_name
mri_to_float
mri_3dalign_setup
3dvolreg main
Bottom of Debug Stack
** AFNI version = AFNI_2011_12_21_1014 Compile date = Dec 26 2014
** [[Precompiled binary =Debian-x86_64-1-gnu: Dec 26 2014]]
** Program Abort **
** If you report this crash to the AFNI message board,
** please copy the error messages EXACTLY, and give
** the command line you used to run the program, and
** any other information needed to repeat the problem.
** You may later be asked to upload data to help debug.
ERROR: 3dvolreg.afni
Invalid null command.

*****************************************************

mareike-desktop:~/ProBrain/functional> afni_system_check.py -check_all -------------------------------- general ---------------------------------
architecture: 64bit ELF
system: Linux
release: 3.13.0-45-generic
version: #74-Ubuntu SMP Tue Jan 13 19:36:28 UTC 2015
distribution: Ubuntu 14.04 trusty
number of CPUs: 4
apparent login shell: bash (current shell is tcsh)

--------------------- AFNI and related program tests ---------------------
which afni : /home/mareike/abin/afni
afni version : Precompiled binary linux_openmp_64: Feb 13 2015
which python : /usr/bin/python
python version : 2.7.6
which R : /usr/bin/R
R version : R version 3.0.2 (2013-09-25) -- "Frisbee Sailing"
which tcsh : /usr/bin/tcsh

instances of various programs found in PATH:
afni : 1 (/home/mareike/abin/afni)
R : 1 (/usr/bin/R)
python : 1 (/usr/bin/python2.7)

testing ability to start various programs...
afni : success
suma : success
3dSkullStrip : success
uber_subject.py : success
3dAllineate : success
3dRSFC : success
SurfMesh : success

checking for $HOME files...
.afnirc : found
.sumarc : found
.afni/help/all_progs.COMP : found

------------------------------ python libs -------------------------------
++ module 'PyQt4' found at /usr/lib/python2.7/dist-packages/PyQt4
++ module loaded: PyQt4

------------------------------- path vars --------------------------------
PATH = /usr/local/freesurfer/bin:/usr/local/freesurfer/fsfast/bin:/usr/local/freesurfer/tktools:/usr/local/freesurfer/mni/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games:/home/mareike/abin

PYTHONPATH =
LD_LIBRARY_PATH =
DYLD_LIBRARY_PATH =
DYLD_FALLBACK_LIBRARY_PATH =

------------------------------ data checks -------------------------------
data dir : missing AFNI_data6
data dir : missing suma_demo
atlas : found TT_N27+tlrc under /home/mareike/abin
atlas : found TT_N27+tlrc under /usr/share/afni/atlases

------------------------------ OS specific -------------------------------
have Ubuntu system: Ubuntu 14.04 trusty

---------------------------- general comments ----------------------------

I wonder if I should install an OLDER Afni version? After all, the error first occured when I tried to update afni? I would really appreciate further advice.