If you have age groups like 20-29, 30-39; it becomes ordinal. Association between ordinal and a nominal is captured through Chi-square (a non parametric test).

regards

I think you want multinomial logistic regression--the NOMREG procedure in SPSS.  There's an annotated example at the link below.  It uses a DV with 3 categories, but you should get the idea.

http://www.ats.ucla.edu/stat/spss/output/mlogit.htm

I think that ordinal logistic regression in SPSS is the most suitable for your problem

Lydia, note that Calli said the outcome (dependent) variable was nominal, not ordinal. 

"Which is a suitable test in SPSS to test the relationship between a continuous (ID-age) and a nominal (DV) variable if the data is not normal?"  (Emphasis added)

Participants' age is which is the IV (not-normally distributed) is not in groups (age represents individually each participant's years of age, not in order). My DV is nominal with 4 values ( yellow, dark, unsure, other). Thanks for advising. Really appreciating it.

Bruce Weaver i just want to thank you, the NOMREG worked beautifully. Thank you again. 

You can apply One way analysis of variance ANOVA to test the significance of  differences between ID-age means for DV groups (levels)