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We present in Part II the description of the internal degrees of freedom offermions by the superposition of odd products of the Clifford algebra elements,either $\gamma^a$'s or $\tilde{\gamma}^a$'s, which determine with their oddnessthe anticommuting properties of the creation and annihilation operators of thesecond quantized fermion fields in even $d$-dimensional space-time, as we do inPart I of this paper by the Grassmann algebra elements $\theta^a$'s and$\frac{\partial}{\partial \theta_a}$'s. We discuss: {\bf i.} The properties ofthe two kinds of the odd Clifford algebras, forming two independent spaces,both expressible with the Grassmann algebra of $\theta^{a}$'s and$\frac{\partial}{\partial \theta_{a}}$'s. {\bf ii.} The freezing out procedureof one of the two kinds of the odd Clifford objects, enabling that theremaining Clifford objects determine with their oddness in the tensor productsof the finite number of the Clifford basis vectors and the infinite number ofmomentum basis, the creation and annihilation operators carrying the familyquantum numbers and fulfilling the anticommutation relations of the secondquantized fermions: on the vacuum state, and on the whole Hilbert space definedby the sum of infinite number of "Slater determinants" of empty and occupiedsingle fermion states. {\bf iii.} The relation between the second quantizedfermions as postulated by Dirac and the ones following from our Cliffordalgebra creation and annihilation operators, what offers the explanation forthe Dirac postulates.

Understanding the second quantization of fermions in Clifford and in Grassmann space -- New way of second quantization of fermions, Part II