Hopelessness can be consider as a subtype of depressions, it can be defined as having no expectation of good or success, giving no ground for hope, incapable of solution management or accomplishment .

Hopelessness is one of psychological variables that distinguish negative personalities because there are positive correlation between hopelessness and variables such as : anxiety, depression, suicide thought and so on .

One of the important variables correlate with hopelessness is low self-esteem, many studies indicate that there are statistically significant inverse relationship between the two variables, the present study aimed to :

1. Measures hopelessness for university students.
2. Acquaint to the significant of differences between males and females and scientific college students and humanistic college students .
3. Measures self-esteem of university student .
4. Acquaint to the significant of differences between males and females and between scientific college students and humanistic college students .
5. Acquaint to the relationship between hopelessness and self-esteem for university students .

To a chive this aims is should used two instruments, the first to measure hopelessness that is Al-Jaberi scale ( 2007 ) consist of ( 20 ) items, the face validity of this scale in this research obtained, also reliability in internal consistency ( Alph coefficient ) method at value ( 0.77 ).

The second scale for measure self-esteem it was Al-Ubaide scale ( 1999 ), consist of (  36 ) items, the face validity of this scale in this research obtained as well as reliability in internal consistency ( split – half ) at the value of ( 0.64 ) .

The two scales applied on sample consisting of ( 138 ) student ( males and females ) from Baghdad university for academic year 2008 – 2009, after the data have been statically treated by adopting the appropriate means such as t – test for one sample and for two separate samples and Pearson correlation coefficient, the result was:

1. There are no hopelessness for university students in this research, and this is a positive indicate of psychological health.
2. There are no statistical significant differences between males and females and between scientific college student and humanistic college student in regard to hopelessness.
3. The total level of self-esteem for university students in this research is high, this is a positive indicate of psychological health for them.
4. There are no statistical significant differences between males and females and between scientific college student and humanistic college student in regard to self-esteem.
5. There are statistically significant inverse relationship between hopelessness and self-esteem for university student.

According to the above results, number of recommendations and suggestions have presented.