I am 99% sure yes, IF, they are both Saginaw 800 boxes. The Saginaw 600's are goofy and don't always directly interchange with the 800s.
Some good reading here:
http://www.classicperform.com/tech_articles/turn-turn-turn/turn-turn-turn.htm
http://www.popularhotrodding.com/tech/0512phr_1976_chevrolet_camaro_steering_box_install/ (remember, your 78 front suspension is identical to the same year F Body. And most everything else 70-81 F, 73-77 A/G, 71-76 B/C/D and 77-96 B/D. The differences are primarily in the 1980 timeframe where Metric came into the picture. Even tie rods got a metric taper on the seats.
So here is a repost from
Canuck:
Maybe this is of some help !
GM Box Interchange
A list of direct bolt-on boxes and some that need modifications. (Note this list refers to Saginaw 605 Power boxes but would probably apply to manual as well.
Interchange #706
Buick Special 64-70 Camaro 67-74 Chevelle 64-70
Chevy 65-70 Firebird 67-73 Grand Prix 69-70
Monte Carlo 70 Monza 75-79, 8cyl Monza 78-80,6cyl
Nova 68-70 Olds 64-70 F-85 64-70
Pontiac 64-70 Skyhawk 75-80 Starfire 75
Starfire 76-80, 6 cyl Starfire 77-79, 8cyl Sunbird 76-80
Tempest 64-70
Fast Ratio Box: 20/1 # 7806396 Cast No. 5679142
Monza/Vega Box: 16/1 # 7819935
On some 64-70 the drag link hole on the pitman arm may need to be enlarged.
The following boxes will fit but may need to have the pitman arm and/or the rag joint changed or and extra bolt hole boss taked off the steering box. Make sure you compare the input shaft length or the length from the bolt holes to the end of the input shaft to your power box.
Interchange #999
Apollo 73-75 Omega 73-79
Chevelle 71-77 Skylark 75-79
Monte Carlo 71 Regal 73-74
F-85 71-72 Nova 71-79
Lemans 72-77 Cutlass 76
Ventura 71-77 Phoenix 77-79
Century 73-74 Tempest 71
GMC Sprint 71-77
Cutlass 73
Interchange #989
AMC Ambassador 70-2
AMC 77-80
AMC Spirit 79-83
AMC Hornet 70-77
AMC Concord 78-83
AMC Matador 71-76
AMC Gremlin 70-78
Interchange #1034
Jeepster 72
Jeep 73-83
Jeep CJ & DJ 72
Jeep CJ 84-86
List was derived from Hollander Interchange Manual
Fast ratio Power Steering- Saginaw 605
Use box from 1977-81 Camaro/Firebird with disc brakes (or any 800 series box used in Novas, full size GM, etc), gives approx 3 turns lock to lock, versus original power steering 4.5 turns.
All later model boxes require the 1964 - 72 Chevelle pitman PS arm (required change) when used on earlier Chevelles.
Steering shaft comes in two diameters, get the appropriate flex coupling lower half in the same style as original to match the boxes shaft.
1982 or 86 to 92 Comaro Z-28/firebird Trans-AM are 2 turns (12:1) lock to lock, Use original end cap to get the right stops on 2 turn boxes to decrease turning radius.
Later model boxes (1980 and up) use “O” rings instead of flared input and output lines.
Later model internals can be swapped into early boxes to eliminate problems with line fittings and stops or pump can be modified by changing outlet valve (this requires verification) or swapped to accept "O" ring hosed.
If you are looking at a conversion for a 3x5, I have some dat aon that as well, let me know.
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