Sears, Roebuck & Co., already the nation's largest retailer, today took its second major step in less than a week toward becoming one of the most important forces in the nation's financial services industry with a bid to buy the Wall Street brokerage firm of Dean Witter Reynolds for approximately $600 million.

Sears announced this evening that it will buy the nation's fifth-biggest brokerage firm in a cash and stock deal. As much as $270 million of the purchase price could be paid in cash.

Boards of directors of both Sears and Dean Witter approved the merger and late today signed a merger agreement.

Sears announced Monday it will buy Coldwell Banker & Co., the biggest independent real estate company in the nation for $179 million in cash and Sears stock. Coldwell, whose revenues were $345 million last year, has a nationwide string of real estate brokerage offices. It has done business in the Washington area since 1976 when it bought the Virginia real estate firm Routh Robbins.

Sears has said for the last several months that it wants to become a major factor in the nation's financial services industry, especially for consumers.

The acquisition of Dean Witter, assuming the merger takes place, fulfills that wish. The $25.2 billion Sears, with its nationwide network of 859 retail stores and 25 million credit card customers, overnight will become one of the biggest stock brokers and real estate companies in the nation.

For years Sears has been a major player in parts of the financial services industry. It owns Allstate Insurance, one of the nation's biggest insurance companies that last year had revenues of more than $6 billion. Its Allstate Savings and Loan Association of California has about $2.3 billion in assets. Through its Seraco group (which includes the S&L) it is involved in shopping center and other commercial real estate construction as well as in mortgage insurance.

Last month Sears announced that it planned to start its own money market mutual fund that it would market to its credit card customers. Whether it will market that fund through Dean Witter as well, remains to be seen.

Edward R. Telling, chairman of the Chicago-based Sears, said the company would begin its offer to pay $50 a share in cash for up to 45 percent of the 12.14 million outstanding Dean Witter shares by Oct. 15. The shares of Dean Witter not bought for cash will be exchanged for Sears stock worth approximately $50 assuming a special meeting of Dean Witter stockholders approves the merger. At current prices, a holder of Dean Witter stock would receive 3.1 shares of Sears for each share of Dean Witter.

According to the Sears announcement, Dean Witter will become an autonomous operating entity within the Sears corporate structure and will continue to operate under the Dean Witter Reynolds name. Dean Witter Reynolds is the product of a 1978 merger between Dean Witter and Reynolds Securities.

Dean Witter operates several offices in the Washington area. Last year the brokerage firm had revenues of $251.5 million and net income of $10.6 million. Although it ranks fifth in the total amount of capital it has on hand, its 295 offices place it second among the major brokerage firms, behind Merrill Lynch & Co., the biggest broker in the nation by any measure.

The Sears acquisition of Dean Witter and Coldwell is the latest manifestation of a growing trend toward consolidation in the financial services industry, as companies seek to provide customers with more and more services under one financial roof.

Merrill Lynch began the trend in the 1970s and the nation's biggest broker became a major factor in insurance, real estate brokerage and executive relocation. Merrill Lynch, through its so-called cash-management accounts, also offers de facto banking services to many of its customers.

This year financial services firms have been combining at a swift pace. Prudential Insurance Co., the nation's largest, bought the Bache Group Inc., the sixth-biggest broker. American Express, best-known for its travel cards but also the owner of the Firemen's Fund insurance companies, acquired Shearson Loeb Rhoades, the second-biggest broker.

Phibro Corp., the world's largest publicly traded commodities firm, acquired Salomon Brothers, the big investment banking firm, while the investment banking company Donaldson, Lufkin & Jenrette bought the commodity firm ACLI International. A firm affiliated with the giant Bechtel Corp., the San Francisco-based construction and engineering giant, bought controlling interest in Dillon, Read & Co., an old-line investment banking firm.

Sears' interest in diversifying beyond retailing and insurance was triggered by its inability to grow much more in the retailing field. Sears' position is so dominant in merchandising that its market share cannot grow much more. graphics: WP photo by Harold Flecknoe. Hyatt's newest Regency Hotel, above, opened its doors this week across the street from Baltimore's celebrated Harborplace. But just as this angular chrome-and-glass expanse is not an ordinary looking hotel, neither was it an ordinary hotel opening. Mayor William D. Schaefer arrived in a vintage 1937 Yellow Cab, and proclaimed the hotel would help make Baltimore "a great convention city." Reciprocating. A.M. Pritzker, Regency chain founder, exclaimed, "There ain't nobody like your mayor." Even the hotel's operation is unusual: Out of 550 employes on the staff, 164 are former CETA workers.