The Intel 80376, introduced January 16, 1989, was a variant of the Intel 80386SX intended for embedded systems.
It differed from the 80386 in not supporting real mode

Real mode

Real mode, also called real address mode, is an operating mode of 80286 and later x86-compatible CPUs. Real mode is characterized by a 20 bit segmented memory address space and unlimited direct software access to all memory, I/O addresses and peripheral hardware...

 (the processor booted directly into protected mode

Protected mode

In computing, protected mode, also called protected virtual address mode, is an operational mode of x86-compatible central processing units...

) and having no support for paging in the MMU

Memory management unit

A memory management unit , sometimes called paged memory management unit , is a computer hardware component responsible for handling accesses to memory requested by the CPU...

. The 376 was available at 16 or 20 MHz.

It was replaced with the much more successful 80386EX

Intel 80386EX

The Intel 80386EX is a variant of the Intel 386 microprocessor designed for embedded systems. Introduced in August 1994 and was successful in the market being used aboard several orbiting satellites and microsatellites....

from 1994, and was finally discontinued on June 15, 2001.