Weakness in oil prices and the oil service industry has not discouraged Coniston Partners from accumulating a major stake in NL Industries Inc., a giant oil services and chemicals company.

Coniston, a New York investment partnership headed by Augustus Oliver, Keith Gollust and Paul Tierney, specializes in buying stocks of companies whose assets may be undervalued by the stock market. Wall Street analysts said that, despite the depressed state of NL's drilling-fluid and other oil service operations, the company's valuable chemical businesses attracted Coniston's $70 million investment for 8.23 percent of NL.

"We often find the best stock market values are in industries which are depressed," Gollust said yesterday. "It was the fact that NL's oil service business was complemented by such a strong chemicals business that caused us to be particularly attracted."

Coniston, which accumulated its stake in NL over the last few months, made a pretax profit of $40 million on its $41 million investment last year in Storer Communications Corp. Coniston profited on its 5.3 percent stake in Storer after launching a fight that led to the sale of the company. In Storer and in earlier deals, Coniston's partners have forced managements to take steps that increase shareholder value.

Coniston, which purchased its stake in NL for about $13.70 a share, has requested a meeting with the company's management. NL had no comment yesterday. The stock closed at 15 1/2, unchanged.

NL's "crown jewel," or most valuable businesses, is its titanium dioxide pigments business. Titanium dioxide is a chemical used as a brightening ingredient in paints, plastics and paper. Analyst said that, while NL's oil service businesses are unprofitable, this commodity chemicals business is generating an annual cash flow of about $130 million. If NL were to sell this business, the risk to a buyer would be the possibility that the price of titanium dioxide would drop, because NL and others are expanding their overseas production.

"Most of us looking at NL before (Coniston) came up with a market value for the various parts of $18 or $19 a share," said Elizabeth Peek, an oil service analyst with Wertheim & Co. "There is tremendous uncertainty about the value and expected cash flow of the oil field assets . . . . "

Peek said one attractive element in NL is an overfunded pension plan that has about $120 million of excess cash. Despite this excess cash, Peek said the uncertainty of the cash flow from its oil service businesses does not make NL a good buyout candidate.

"If they sold their chemical businesses, that would leave NL primarily with an oil service company losing money," Salomon Brothers analyst James Crandell said. "NL management in the past has rejected the idea of selling one of the two businesses because it has enjoyed having one business carry them when the other is depressed."

For the nine months that ended Sept. 30, NL had revenue of $1 billion and net income of $16.3 million (23 cents a share) compared with revenue of $1 billion and net income of $11.1 million (14 cents) in the first nine months of 1984.