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Let $\mathcal{I}_{d_1,d_2}$ and $\mathcal{C}_{d_1,d_2}$ be the algebras ofjoint invariants and joint covariants of the two binary forms of degrees $d_1$and $d_2.$ Formulas for computation of the Poincar\'e series$\mathcal{PI}_{d_1,d_2}(z),$ $ \mathcal{PC}_{d_1,d_2}(z)$ of the algebras isfound. By using these formulas, we have computed the series for $d_1,d_2 \leq20.$

The Poincar\'e series of the joint invariants and covariants of the two binary forms