Originating from a disturbance in the Intertropical Convergence Zone in late-August, Uleki was identified as a tropical depression well to the southeast of Hawaii on August 28.

In late-August 1988, increased convective activity was noted along the Intertropical Convergence Zone by forecasters at the Central Pacific Hurricane Center (CPHC).

Steady intensification ensued over the following day with the system attaining gale-force winds by 18:00 UTC on August 29, at which time it was assigned the name Uleki.

[nb 2] After reaching this strength, Uleki's forward motion gradually lessened and eventually almost ceased altogether on September 1 as upper-level steering currents collapsed.

On September 2, they found maximum surface winds of 125 mph (201 km/h) and a minimum barometric pressure of 957 mbar (hPa; 28.26 inHg); this corresponded to the peak intensity of Uleki.

[3] The cyclone's winds dropped to 80 mph (130 km/h) by 12:00 UTC on September 4 as it resumed its west-northwest track under the influence of a subtropical ridge away from the Hawaiian Islands.

A trough approaching from the west was forecast to prompt Uleki to turn east; however, the typhoon maintained a general northwest motion in a stair-stepped fashion.

[4] Continued effects from shear stripped the cyclone of all deep convection, and by September 14 only a band of cirrus clouds remained in association with Uleki.

[2][6] The storm moved roughly halfway between the French Frigate Shoals and Johnston Island on September 5 with no adverse effects in either region due to its weakened state.

[7] Hurricane Uleki ultimately passed 200 mi (320 km) south of Midway Atoll and produced some coastal flooding from increased surf.