The objective of this paper is to study the relative homological properties of contravariantly and covariantly finite subcategories. Some sufficient conditions for
E
x
t
¯
Y
n
A
,
B
≃
E
x
t
¯
X
n
A
,
B
are obtained. We also give the conditions under which the stable categories
C
/
W
/
X
/
W
are one-side triangulated categories.