In this paper we give a construction of operators satisfying q-CCR relations for q > 1: $A\left(f\right)A*\left(g\right)-A*\left(g\right)A\left(f\right)=q^N⟨f,g⟩I$ and also q-CAR relations for q < -1: $B\left(f\right)B*\left(g\right)+B*\left(g\right)B\left(f\right)={\left|q\right|}^N⟨f,g⟩I$, where N is the number operator on a suitable Fock space ${ℱ}_q\left(\right)$ acting as Nx₁ ⊗ ⋯ ⊗ xₙ = nx₁ ⊗ ⋯ ⊗xₙ. Some applications to combinatorial problems are also given.