We give three equational systems of commutative BCK-algebras. The first system CBK I consists of the following three identities: \(((x*y)*(x*z))*(z*y)=0,\quad x*0=x,\quad x*(x*y)=y*(y*x).\) The second system CBK II consists of the following three identities: \(0*x=0\), \(x*0=x\), \((x*y)*(x*z)=(z*y)*(z*x).\) The third system CBK III consists of the following three identities: \(x*x=0\), \(x*0=x\), \((x*y)*(x*z)=(z*y)*(z*x).\)