Two of the nation's leading tire and rubber manufacturers, Goodyear Tire and Rubber Co. and B. F. Goodrich Co., yesterday reported lower fourth-quarter profits, but strong gains for the year.

Goodyear, the largest U.S. tiremaker, said its profits for the quarter were off 22 percent at $42.4 million (50 cents a share) against the year-ago period's $54.2 million (75 cents). Sales were up 13 percent to $1.7 billion from $1.5 billion.

For all of 1977, Goodyear's profits were $205.8 million ($2.85), 70.6 percent from 1976's $120.6 million ($1.67). Sales rose 13.7 percent to $6.6 billion from $5.8 billion.

Goodyear said competitive price cutting and oversupply of both original equipment tires (for new cars) and replacement tires depressed profits in the fourth quarter. It said this was partly offset by the success of its all-season Tiempo tire.

Goodyear also noted that it had currency translation losses in 1977 of $47 million, reflecting the decline of the dollar, against a $13 million foreign currency translation loss in 1976.

Figures for 1976 reflected a four-month strike by the United Rubber-workers Union.

Goodyear said it plans to spend about $400 million on new plant and equipment this year, one-third more than in 1977.

B. F. Goodrich said its fourth-quarter profits plunged 74 percent to $5.9 million (37 cents a share) from $22.8 million ($1.53) in the year-ago period Sales were up 6 percent to $540.8 million from $510.3 million.

For the year, however, profits nearly quadrupled to $60.1 million $3.97 from 1976's $15.8 million (95 cents). Sales were up 10 percent to $2.2 billion from $12 billion.

Goodrich's 1977 profits broke the previous record of $58.9 million set in 1973. Sales in nearly all areas were strong last year, and tires and related products were expecially strong.