The notion of an essentially slant Toeplitz operator on the space $L^2$ is
introduced and some of the properties of the set ${\rm ESTO}(L^2)$, the set of
all essentially slant Toeplitz operators on $L^2$, are investigated. In
particular the conditions under which the product of two operators in ${\rm
ESTO}(L^2)$ is in ${\rm ESTO}(L^2)$ are discussed. The notion is generalized to
$k$th-order essentially slant Toeplitz operators.