Abstract
A non-symmetric version of a symmetric operad is defined as the operad of algebras, where all consequences of the identity of degree 2 are valid in degree higher than 2 and not valid in degree 2. The main identity that should be included for such an operad is the reverse-associative identity $$a(bc)=(cb)a$$. An algebra is $$\pm$$-Jacobi admissible and $$\pm$$-associative-admissible if it satisfies the Jacobi identity and the associative identity under $$\pm$$-commutators, respectively. In our paper we consider operads related to Lie-admissible, associative-admissible, and associative-Lie-admissible algebras. In particular we find the dimension sequences of their multilinear parts.