The kit for the detection of SNPs in the promoter III region of the gene of acetyl-CoA carboxylase (ACACA) in sheep by the polymerase chain reaction at the level of genomic DNA, and then followed by a SnaPshot miniseccation which is characterized by comprising primers with the composition of ov-ACACA F: 5´-ggg CCC CTT TAC gTT TCT gT – 3´, ov-ACACA R: 5´ – AgC TTC TgC CTT AgC TgC A- 3 ´ of the amplicon length of 513 bp, and, further, an extension primer for the detection of a new genetic polymorphism at the 1168 bp A/G position of the Ov-acaca Sh1 composition: 5´- (AT)2gTg gTg gCg TgT CTC – 3´. The set further includes a set of extension primers with the composition Ov-acaca Sh2: 5´- (AT)3gCA TAg CTg TCC TCg TAA gC – 3´, Ov-acaca Sh3: 5´- (AT)6gAA ggC TCA ggg CAA AAA gA – 3´, Ov-acaca Sh4: 5´- (AT)8gAC CgT CAg AAg AAA gTg AC – 3´ for multiplex detection of genetic variants at the position of 1330 bp G/T, 1338 bp C/G and 1430 bp C/T.