NEW YORK – The long slide of T-Mobile USA continued in the latest quarter, as the country’s No. 4 cellphone company lost subscribers and struggled to sign people up for smartphones.

The company, a subsidiary of Germany’s Deutsche Telekom AG, said Thursday that it lost a net 205,000 subscribers in the second quarter, a record for the period.

Among phone subscribers under contract, it lost 557,000 subscribers, also the highest number of the second quarter.

T-Mobile’s revenue from monthly fees on contract service fell 9 percent from a year ago. The larger wireless carriers — Verizon, AT&T and Sprint — all managed to increase this number in the second quarter.

While other big carriers rely on boosting smartphone use to raise monthly fees, the number of smartphone users at T-Mobile USA was flat from the first quarter, at 11.6 million.