Recent advances in single nucleotide polymorphisms (SNPs) research have raised the possibility that these markers could replace the forensically established short tandem repeats (STRs). In this work, we compare STRs and SNPs applicability for kinship investigation in terms of expected informative content and probability of occurrence of "difficult cases" (when isolated Mendelian incompatibilities between alleged father and child are found). Since SNPs have a much lower mutation rate than STRs, these difficulties were expected to occur less frequently if SNPs were used instead of STRs. The purpose of this paper is to make some simulations allowing the estimation of how often such difficult cases are expected to occur using both types of markers and how serious can be their impact in routine work. Our results demonstrate that a battery based exclusively on SNPs matching the informative power of current STR kits would be prone, if applied to routine paternity investigation, to the occurrence of cases where the statistical evidence would be inconclusive. We infer that the introduction of a SNP based strategy, as a substitute to the now classical STR approach poses statistical problems that must be carefully evaluated.