Let
A
A
be a representation-finite algebra. We show that a finite dimensional
A
A
-module
M
M
degenerates to another
A
A
-module
N
N
if and only if the inequalities
dim
K
H
o
m
A
(
M
,
X
)
≤
dim
K
H
o
m
A
(
N
,
X
)
\dim _{K} Hom_{A}(M,X)\leq \dim _{K} Hom_{A}(N,X)
hold for all
A
A
-modules
X
X
. We prove also that if
Ext
A
1
(
X
,
X
)
=
0
\operatorname {Ext}_{A}^{1}(X,X)=0
for any indecomposable
A
A
-module
X
X
, then any degeneration of
A
A
-modules is given by a chain of short exact sequences.