In the late 1970s, the Soviets realised the need for a larger, more seaworthy craft with better gun armament and higher positioned air search radars.

A version of these ships for coastal anti-submarine warfare and patrol was developed as the Pauk-class corvette or Project 1241.2.

Instead, the fire control radar, X-band "Garpun-Bal" (NATO: "Plank Shave"), built for the anti-ship missiles, was installed on the top of the mast.

The model of the missiles in the KT-138 launch containers were P-20 (NATO: SS-N-2B), basically they were P-15 updated with the new guidance system but with the original 40 km range.

Apart from a modest but useful internal redesign, the Tarantul-III had a new type of propulsion—a CODAG (COmbined Diesel And Gas) system.

Two M-70 gas turbines (rated at 12,000 hp each) and two M510 (rated at 4,000 hp each) diesel engines were used, being a big improvement over the earlier COGOG system both in terms of serviceability (the two cruise diesels being almost something of a Soviet 'classic'), fuel efficiency and, most importantly, service life expectancy compared to the older NK-12Ms.

The superstructures were redesigned and the angled mast of the previous projects has been replaced by a narrow, straight lattice.

The missiles can also receive third party guidance through the 'Light Bulb' uplink (from other ships, helicopters or long range patrol aircraft).

After the construction of first batch of 11 ships, the anti-ship missiles were changed from the P-80 "Moskit" to the more modern model P-270 "Moskit-M", therefore the following 23 boats had a new ID: Project 1241.1MR.

The two projects has been modified and rearmed with modern missile systems like the Uran-E and are more capable ships than the Tarantul types.

Vietnam started its own production line of 1241.8 Molniya ships with the assistance of Almaz Central Design Bureau in Russia.

These last two ships of the Veer class are armed with 16 SS-N-25 'Switchblade' / URAN E missiles, a OTO Melara 76 mm gun instead of the AK-176, and MR 352 Positiv-E (NATO: Cross Dome) radar.

[4][5] In 2009 Libya ordered three ships,[citation needed] however, the civil war in 2011 put a stop to any acquisitions.