We define and study generalized nil-Coxeter algebras associated to Coxeter groups. Motivated by a question of Coxeter (1957), we construct the first examples of such finite-dimensional algebras that are not the “usual” nil-Coxeter algebras: a novel
2
2
-parameter type
A
A
family that we call
N
C
A
(
n
,
d
)
NC_A(n,d)
. We explore several combinatorial properties of
N
C
A
(
n
,
d
)
NC_A(n,d)
, including its Coxeter word basis, length function, and Hilbert–Poincaré series, and show that the corresponding generalized Coxeter group is not a flat deformation of
N
C
A
(
n
,
d
)
NC_A(n,d)
. These algebras yield symmetric semigroup module categories that are necessarily not monoidal; we write down their Tannaka–Krein duality.
Further motivated by the Broué–Malle–Rouquier (BMR) freeness conjecture [J. Reine Angew. Math. 1998], we define generalized nil-Coxeter algebras
N
C
W
NC_W
over all discrete real or complex reflection groups
W
W
, finite or infinite. We provide a complete classification of all such algebras that are finite dimensional. Remarkably, these turn out to be either the usual nil-Coxeter algebras or the algebras
N
C
A
(
n
,
d
)
NC_A(n,d)
. This proves as a special case—and strengthens—the lack of equidimensional nil-Coxeter analogues for finite complex reflection groups. In particular, generic Hecke algebras are not flat deformations of
N
C
W
NC_W
for
W
W
complex.