Continuous groups with antilinear operations of the form $G+a_0G$, where $G$ denotes a linear Lie group, and $a_0$ is an antilinear operation which fulfills the condition $a^2_0=pm 1$, were defined and their matrix algebras were investigated in cite{
Kocinski4}. In this paper infinitesimal-operator algebras are defined for any group of the form $G+a_0G$, and their properties are determined.
Continuous groups of the form: $G+a_0G$ are defined, where $G$ denotes a Lie group and $a_0$ denotes an antilinear operation which fullfils the condition $a^2_0=pm 1$. The matrix algebras connected with the groups $G+a_0G$ are defined. The structural
constants of these algebras fulfill the conditions following from the Jacobi identities.
