In this paper, we investigate slice holomorphic functions of several complex variables having bounded L-index in a direction, i.e. we consider functions which are entire on every slice {<$Ez sup 0 ~+~t roman bold b~:~t~symbol <174>~C>} for every <$Ez sup 0 ~symbol <174>~C sup n> and for a given direction <$Eroman bold b~symbol <174>~C sup n> \ {0}. For this function class we prove some criteria of boundedness of L-index in the direction describing local behavior of maximum modulus, minimum modulus of the slice holomorphic function and providing estimates of logarithmic derivative and distribution of zeros. Moreover, we obtain analogs of known Hayman's theorem and logarithmic criteria. They are applicable in analytic theory of differential equations. We also investigate value distribution of these functions and present existence theorem for this function class. It indicates that bounded multiplicity of zeros for slice holomorphic function <$EF~:~C sup n ~symbol О~C> is the necessary and sufficient condition for existence of a positive continuous function <$EL~:~C sup n ~symbol О~ R sub +> such that F has bounded L-index in the direction.

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