How to comprehend allele?

I do have a knowledge that allele is either of a pair of genes that occupies the specific locus,according to which there is no doubt that in such a genotype, for example DD, there exist alleles.However, recently someone has just told me that in such a genotype of DD or some else of double identical genes there are no alleles at all. Whereupon I really wonder which opinion is right? Thanks for help!