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We prove the existence of C0 semigroups related to some birth-and-death type infinite systems of ODEs with possibly unbounded coefficients, in the scale of spaces lp, $1\leq p<\infty.$ For some particular cases we also provide a characterization of the spectra of their generators. For the proof of the generation theorem in the case p > 1 we extend the Chernoff perturbation result ([9]) on relatively bounded perturbations of generators. The results presented here have been used in [5] and they play important role for analysing chaoticity of dynamical systems considered there. As a by-product of our approach we obtain a result related to the classical Shubin theorem [20]. We show that this theorem, saying that for a class of bounded infinite matrices the spectrum of the corresponding maximal operator in lp is independent on $p\in [1,\infty),$ cannot be extended to unbounded matrices. [ABSTRACT FROM AUTHOR]