Greig's tenure began promisingly. Wallace's treble-winning team of the previous season performed ably in the European Cup. Juventus were defeated 2-1 on aggregate - the first time Rangers had ever recovered from a first-leg defeat to win a two-legged European tie.
PSV Eindhoven were defeated in the next round (the club's first home defeat in European competition), before an injury-stricken team lost to Cologne in the quarter final. Things began to unravel towards the end of Greig's first domestic season, however, as leadership of the league evaporated. Greig's efforts thereafter to restructure the team inherited from Wallace proved, for the most part, fruitless.
The early years of the 1980s were ones of repeated frustration as the club continually failed to mount a challenge not only to Celtic, but to the then resurgent "New Firm" of Aberdeen and Dundee United. The gloom of under-performance in the league was punctuated only by periodic cup triumphs. The Scottish Cup win of 1981, in particular, saw a triumphant performance by the enigmatic winger, Davie Cooper. The League Cup proved fertile territory for Rangers throughout the fallow years of the early 1980s, but it was the failure to add to the league triumph of 1978 that saw the growing pressure on Greig culminate in his resignation as manager in 1983.