We consider the existence of invariant manifolds to evolution equations
u
′
(
t
)
=
A
u
(
t
)
u’(t)=Au(t)
,
A
:
D
(
A
)
⊂
X
→
X
A:D(A)\subset \mathbb {X}\to \mathbb {X}
near its equilibrium
A
(
0
)
=
0
A(0)=0
under the assumption that its proto-derivative
∂
A
(
x
)
\partial A(x)
exists and is continuous in
x
∈
D
(
A
)
x\in D(A)
in the sense of Yosida distance. Yosida distance between two (unbounded) linear operators
U
U
and
V
V
in a Banach space
X
\mathbb {X}
is defined as
d
Y
(
U
,
V
)
≔
lim sup
μ
→
+
∞
‖
U
μ
−
V
μ
‖
d_Y(U,V)≔\limsup _{\mu \to +\infty } \| U_\mu -V_\mu \|
, where
U
μ
U_\mu
and
V
μ
V_\mu
are the Yosida approximations of
U
U
and
V
V
, respectively. We show that the above-mentioned equation has local stable and unstable invariant manifolds near an exponentially dichotomous equilibrium if the proto-derivative of
∂
A
\partial A
is continuous in the sense of Yosida distance. The Yosida distance approach allows us to generalize the well-known results with possible applications to larger classes of partial differential equations and functional differential equations. The obtained results seem to be new.